
@article{AgmonDouglisNirenberg1959,
  author = {Agmon, Shmuel and Douglis, Avron and Nirenberg, Louis},
  doi = {10.1002/cpa.3160120405},
  journal = {Communications on Pure and Applied Mathematics},
  month = {November},
  number = {4},
  pages = {623--727},
  title = {Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. {I}},
  url = {https://onlinelibrary.wiley.com/doi/10.1002/cpa.3160120405},
  volume = {12},
  year = {1959}
}

@article{AgmonDouglisNirenberg1964,
  author = {Agmon, Shmuel and Douglis, Avron and Nirenberg, Louis},
  doi = {10.1002/cpa.3160170104},
  journal = {Communications on Pure and Applied Mathematics},
  number = {1},
  pages = {35--92},
  title = {Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. {II}},
  url = {https://onlinelibrary.wiley.com/doi/10.1002/cpa.3160170104},
  volume = {17},
  year = {1964}
}

@article{Allard1972,
  author = {Allard, William K.},
  title = {On the First Variation of a Varifold},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {95},
  number = {3},
  pages = {417--491},
  year = {1972},
  doi = {10.2307/1970868},
  url = {https://www.jstor.org/stable/1970868}
}

@misc{AllenBrydenKazarasKhuri2025,
  archiveprefix = {arXiv},
  author = {Allen, Brian and Bryden, Edward and Kazaras, Demetre and Khuri, Marcus},
  doi = {10.48550/arXiv.2504.10641},
  eprint = {2504.10641},
  primaryclass = {math.DG},
  title = {Proof of the Spacetime {Penrose} Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes},
  url = {https://arxiv.org/abs/2504.10641},
  year = {2025}
}

@book{AmbrosioFuscoPallara2000,
  address = {Oxford},
  author = {Ambrosio, Luigi and Fusco, Nicola and Pallara, Diego},
  doi = {10.1093/oso/9780198502456.001.0001},
  isbn = {9780198502456},
  publisher = {Oxford University Press},
  series = {Oxford Mathematical Monographs},
  title = {Functions of Bounded Variation and Free Discontinuity Problems},
  url = {https://academic.oup.com/book/53762},
  year = {2000}
}

@article{Ambrozio2015,
  archiveprefix = {arXiv},
  author = {Ambrozio, Lucas C.},
  doi = {10.1007/s00220-015-2360-6},
  eprint = {1402.4317},
  journal = {Communications in Mathematical Physics},
  number = {2},
  pages = {767--783},
  primaryclass = {math.DG},
  title = {On perturbations of the {Schwarzschild anti-de Sitter} spaces of positive mass},
  url = {https://doi.org/10.1007/s00220-015-2360-6},
  volume = {337},
  year = {2015}
}

@incollection{AnderssonEichmairMetzger2011,
  address = {Providence, RI},
  author = {Andersson, Lars and Eichmair, Michael and Metzger, Jan},
  booktitle = {Complex Analysis and Dynamical Systems {IV}.
Part 2: General Relativity, Geometry, and {PDE}},
  doi = {10.1090/conm/554/10958},
  note = {Theorem numbering refers to arXiv:1006.4601v2},
  pages = {13--45},
  publisher = {American Mathematical Society},
  series = {Contemporary Mathematics},
  title = {{Jang}'s equation and its applications to marginally trapped surfaces},
  url = {https://arxiv.org/abs/1006.4601v2},
  volume = {554},
  year = {2011}
}

@article{AnderssonMarsSimon2008,
  archiveprefix = {arXiv},
  author = {Andersson, Lars and Mars, Marc and Simon, Walter},
  doi = {10.4310/ATMP.2008.v12.n4.a5},
  eprint = {0704.2889},
  journal = {Advances in Theoretical and Mathematical Physics},
  number = {4},
  pages = {853--888},
  title = {Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes},
  url = {https://archive.intlpress.com/site/pub/files/_fulltext/journals/atmp/2008/0012/0004/ATMP-2008-0012-0004-a005.pdf},
  volume = {12},
  year = {2008}
}

@article{AnderssonMetzger2009,
  archiveprefix = {arXiv},
  author = {Andersson, Lars and Metzger, Jan},
  doi = {10.1007/s00220-008-0723-y},
  eprint = {0708.4252},
  journal = {Communications in Mathematical Physics},
  number = {3},
  pages = {941--972},
  title = {The area of horizons and the trapped region},
  url = {https://link.springer.com/content/pdf/10.1007/s00220-008-0723-y.pdf},
  volume = {290},
  year = {2009}
}

@incollection{ArnowittDeserMisner1962,
  address = {New York},
  archiveprefix = {arXiv},
  author = {Arnowitt, Richard and Deser, Stanley and Misner, Charles W.},
  booktitle = {Gravitation: An Introduction to Current Research},
  chapter = {7},
  editor = {Witten, Louis},
  eprint = {gr-qc/0405109},
  note = {Electronic reprint; original section and equation numbering retained},
  pages = {227--265},
  publisher = {Wiley},
  title = {The dynamics of general relativity},
  url = {https://arxiv.org/abs/gr-qc/0405109},
  year = {1962}
}

@article{Bartnik1986,
  author = {Bartnik, Robert},
  doi = {10.1002/cpa.3160390505},
  journal = {Communications on Pure and Applied Mathematics},
  number = {5},
  pages = {661--693},
  title = {The mass of an asymptotically flat manifold},
  url = {https://math.jhu.edu/~js/Math646/bartnik.mass.pdf},
  volume = {39},
  year = {1986}
}

@article{BartnikChrusciel2005,
  archiveprefix = {arXiv},
  author = {Bartnik, Robert A. and Chru{\'s}ciel, Piotr T.},
  doi = {10.1515/crll.2005.2005.579.13},
  eprint = {math/0307278},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  note = {Theorem numbering follows the author manuscript (July 21, 2003)},
  pages = {13--73},
  title = {Boundary value problems for {Dirac}-type equations},
  url = {https://homepage.univie.ac.at/piotr.chrusciel/papers/dirac/Dirac23.pdf},
  volume = {579},
  year = {2005}
}

@article{BeigChrusciel1996,
  author = {Beig, Robert and Chru{\'s}ciel, Piotr T.},
  title = {Killing Vectors in Asymptotically Flat Space-Times. {I}. {Asymptotically} Translational {Killing} Vectors and the Rigid Positive Energy Theorem},
  journal = {Journal of Mathematical Physics},
  volume = {37},
  number = {4},
  pages = {1939--1961},
  year = {1996},
  doi = {10.1063/1.531497},
  url = {https://arxiv.org/abs/gr-qc/9510015v3}
}

@article{BeigChrusciel1997KID,
  author = {Beig, Robert and Chru{\'s}ciel, Piotr T.},
  title = {Killing Initial Data},
  journal = {Classical and Quantum Gravity},
  volume = {14},
  number = {1A},
  pages = {A83--A92},
  year = {1997},
  doi = {10.1088/0264-9381/14/1A/007},
  url = {https://arxiv.org/abs/gr-qc/9604040v1}
}

@article{BenDov2004,
  archiveprefix = {arXiv},
  author = {Ben-Dov, Ishai},
  doi = {10.1103/PhysRevD.70.124031},
  eprint = {gr-qc/0408066},
  journal = {Physical Review D},
  pages = {124031},
  title = {The {Penrose} inequality and apparent horizons},
  url = {https://arxiv.org/abs/gr-qc/0408066},
  volume = {70},
  year = {2004}
}

@article{BenedettiLisca2018,
  author = {Benedetti, Riccardo and Lisca, Paolo},
  doi = {10.4171/LEM/64-3/4-9},
  journal = {L'Enseignement Math{\'e}matique},
  number = {3--4},
  pages = {395--413},
  series = {2},
  title = {Framing {$3$}-manifolds with bare hands},
  url = {https://ems.press/journals/lem/articles/16378},
  volume = {64},
  year = {2018}
}

@book{Besse1987,
  address = {Berlin--Heidelberg--New York},
  author = {Besse, Arthur L.},
  publisher = {Springer-Verlag},
  series = {Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge},
  title = {Einstein Manifolds},
  url = {https://link.springer.com/content/pdf/bfm:978-3-540-74311-8/1},
  volume = {10},
  year = {1987}
}

@article{Bray2001,
  archiveprefix = {arXiv},
  author = {Bray, Hubert L.},
  doi = {10.4310/jdg/1090349428},
  eprint = {math/9911173},
  journal = {Journal of Differential Geometry},
  number = {2},
  pages = {177--267},
  primaryclass = {math.DG},
  title = {Proof of the {Riemannian Penrose} inequality using the positive mass theorem},
  url = {https://doi.org/10.4310/jdg/1090349428},
  volume = {59},
  year = {2001}
}

@article{BrayKhuri2010,
  archiveprefix = {arXiv},
  author = {Bray, Hubert L. and Khuri, Marcus A.},
  doi = {10.3934/dcds.2010.27.741},
  eprint = {0910.4785},
  journal = {Discrete and Continuous Dynamical Systems},
  number = {2},
  pages = {741--766},
  primaryclass = {math.DG},
  title = {A {Jang} equation approach to the {Penrose} inequality},
  url = {https://arxiv.org/abs/0910.4785},
  volume = {27},
  year = {2010}
}

@article{BrayKhuri2011,
  archiveprefix = {arXiv},
  author = {Bray, Hubert L. and Khuri, Marcus A.},
  doi = {10.4310/AJM.2011.v15.n4.a5},
  eprint = {0905.2622},
  journal = {Asian Journal of Mathematics},
  note = {\href{https://doi.org/10.4310/AJM.2011.v15.n4.a5}{doi:10.4310/AJM.2011.v15.n4.a5}},
  number = {4},
  pages = {559--612},
  title = {P.d.e.'s which imply the {Penrose} conjecture},
  url = {https://www.math.stonybrook.edu/~khuri/Khuri_Bray_AsianJMath.pdf},
  volume = {15},
  year = {2011}
}

@article{BrayLee2009,
  author = {Bray, Hubert L. and Lee, Dan A.},
  doi = {10.1215/00127094-2009-020},
  journal = {Duke Mathematical Journal},
  number = {1},
  pages = {81--106},
  title = {On the {Riemannian Penrose} inequality in dimensions less than eight},
  url = {https://math.duke.edu/~bray/PE/euclid.dmj.1240432192.pdf},
  volume = {148},
  year = {2009}
}

@article{Brendle2021,
  author = {Brendle, Simon},
  doi = {10.1090/jams/969},
  journal = {Journal of the American Mathematical Society},
  number = {2},
  pages = {595--603},
  title = {The isoperimetric inequality for a minimal submanifold in {Euclidean} space},
  url = {https://doi.org/10.1090/jams/969},
  volume = {34},
  year = {2021}
}

@article{BuntingMasoodUlAlam1987,
  author = {Bunting, Gary L. and {Masood-ul-Alam}, A. K. M.},
  doi = {10.1007/BF00770326},
  journal = {General Relativity and Gravitation},
  month = {February},
  number = {2},
  pages = {147--154},
  title = {Nonexistence of multiple black holes in asymptotically {Euclidean} static vacuum space-time},
  url = {https://link.springer.com/article/10.1007/BF00770326},
  volume = {19},
  year = {1987}
}

@book{BuragoBuragoIvanov2001,
  address = {Providence, RI},
  author = {Burago, Dmitri and Burago, Yuri and Ivanov, Sergei},
  doi = {10.1090/gsm/033},
  isbn = {0-8218-2129-6},
  publisher = {American Mathematical Society},
  series = {Graduate Studies in Mathematics},
  title = {A Course in Metric Geometry},
  url = {https://bookstore.ams.org/gsm-33},
  volume = {33},
  year = {2001}
}

@article{CarrascoMars2010,
  archiveprefix = {arXiv},
  author = {Carrasco, Alberto and Mars, Marc},
  doi = {10.1088/0264-9381/27/6/062001},
  eprint = {0911.0883},
  journal = {Classical and Quantum Gravity},
  pages = {062001},
  title = {A counter-example to a recent version of the {Penrose} conjecture},
  url = {https://arxiv.org/abs/0911.0883},
  volume = {27},
  year = {2010}
}

@article{CecchiniZeidler2024,
  archiveprefix = {arXiv},
  author = {Cecchini, Simone and Zeidler, Rudolf},
  doi = {10.1090/tran/8942},
  eprint = {2108.11972v2},
  journal = {Transactions of the American Mathematical Society},
  pages = {5271--5288},
  title = {The positive mass theorem and distance estimates in the spin setting},
  note = {Theorem numbering refers to arXiv:2108.11972v2},
  url = {https://arxiv.org/abs/2108.11972v2},
  volume = {377},
  year = {2024}
}

@article{Chern1944,
  author = {Chern, Shiing-Shen},
  doi = {10.2307/1969302},
  journal = {Annals of Mathematics},
  month = {October},
  number = {4},
  pages = {747--752},
  series = {2},
  title = {A simple intrinsic proof of the {Gauss--Bonnet} formula for closed {Riemannian} manifolds},
  url = {https://www.jstor.org/stable/1969302},
  volume = {45},
  year = {1944}
}

@article{ChruscielHerzlich2003,
  archiveprefix = {arXiv},
  author = {Chru{\'s}ciel, Piotr T. and Herzlich, Marc},
  doi = {10.2140/pjm.2003.212.231},
  eprint = {math/0110035},
  journal = {Pacific Journal of Mathematics},
  number = {2},
  pages = {231--264},
  primaryclass = {math.DG},
  title = {The mass of asymptotically hyperbolic {Riemannian} manifolds},
  url = {https://doi.org/10.2140/pjm.2003.212.231},
  volume = {212},
  year = {2003}
}

@article{ChruscielReallTod2006,
  archiveprefix = {arXiv},
  author = {Chru{\'s}ciel, Piotr T. and Reall, Harvey S. and Tod, Paul},
  doi = {10.1088/0264-9381/23/7/018},
  eprint = {gr-qc/0512116},
  journal = {Classical and Quantum Gravity},
  number = {7},
  pages = {2519--2540},
  title = {On {Israel--Wilson--Perj{\'e}s} black holes},
  url = {https://arxiv.org/abs/gr-qc/0512116},
  volume = {23},
  year = {2006}
}

@article{CostabelMcIntosh2010,
  archiveprefix = {arXiv},
  author = {Costabel, Martin and McIntosh, Alan},
  doi = {10.1007/s00209-009-0517-8},
  eprint = {0808.2614},
  journal = {Mathematische Zeitschrift},
  number = {2},
  pages = {297--320},
  title = {On {Bogovski\u{\i}} and regularized {Poincar\'e} integral operators for de {Rham} complexes on {Lipschitz} domains},
  url = {https://arxiv.org/abs/0808.2614},
  volume = {265},
  year = {2010}
}

@article{DainJaramilloReiris2012,
  archiveprefix = {arXiv},
  author = {Dain, Sergio and Jaramillo, Jos{\'e} Luis and Reiris, Mart{\'i}n},
  doi = {10.1088/0264-9381/29/3/035013},
  eprint = {1109.5602},
  journal = {Classical and Quantum Gravity},
  number = {3},
  pages = {035013},
  title = {Area-charge inequality for black holes},
  url = {https://arxiv.org/abs/1109.5602},
  volume = {29},
  year = {2012}
}

@article{DeTurckKazdan1981,
  author = {DeTurck, Dennis M. and Kazdan, Jerry L.},
  title = {Some Regularity Theorems in {Riemannian} Geometry},
  journal = {Annales scientifiques de l'{\'E}cole Normale Sup{\'e}rieure},
  series = {4},
  volume = {14},
  number = {3},
  pages = {249--260},
  year = {1981},
  doi = {10.24033/asens.1405},
  url = {https://numdam.org/articles/10.24033/asens.1405/}
}

@book{Deimling1985,
  address = {Berlin and Heidelberg},
  author = {Deimling, Klaus},
  doi = {10.1007/978-3-662-00547-7},
  publisher = {Springer-Verlag},
  title = {Nonlinear Functional Analysis},
  url = {https://link.springer.com/book/10.1007/978-3-662-00547-7},
  year = {1985}
}

@article{DisconziKhuri2012,
  archiveprefix = {arXiv},
  author = {Disconzi, Marcelo M. and Khuri, Marcus A.},
  doi = {10.1088/0264-9381/29/24/245019},
  eprint = {1207.5484},
  journal = {Classical and Quantum Gravity},
  note = {\href{https://doi.org/10.1088/0264-9381/29/24/245019}{doi:10.1088/0264-9381/29/24/245019}},
  number = {24},
  pages = {245019},
  title = {On the {Penrose} inequality for charged black holes},
  url = {https://www.math.stonybrook.edu/~khuri/Khuri_Disconzi_CQG.pdf},
  volume = {29},
  year = {2012}
}

@misc{Dolmen2026,
  archiveprefix = {arXiv},
  author = {Dolmen, Tuan},
  eprint = {2607.29447},
  howpublished = {Preprint, arXiv:2607.29447v1},
  title = {The {Penrose} inequality with charge for 2-convex initial data sets},
  url = {https://arxiv.org/abs/2607.29447v1},
  year = {2026}
}

@book{Federer1969,
  address = {New York},
  author = {Federer, Herbert},
  publisher = {Springer-Verlag},
  series = {Die Grundlehren der mathematischen Wissenschaften},
  title = {Geometric Measure Theory},
  url = {https://link.springer.com/content/pdf/bfm:978-3-642-62010-2/1},
  volume = {153},
  year = {1969}
}

@article{Federer1970,
  author = {Federer, Herbert},
  doi = {10.1090/S0002-9904-1970-12542-3},
  journal = {Bulletin of the American Mathematical Society},
  number = {4},
  pages = {767--771},
  title = {The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension},
  url = {https://www.math.stonybrook.edu/~bishop/classes/math638.F20/Federer_Regularity.pdf},
  volume = {76},
  year = {1970}
}

@article{GibbonsIdaShiromizu2002,
  author = {Gibbons, Gary W. and Ida, Daisuke and Shiromizu, Tetsuya},
  title = {Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions},
  journal = {Progress of Theoretical Physics Supplement},
  volume = {148},
  pages = {284--290},
  year = {2002},
  doi = {10.1143/PTPS.148.284},
  url = {https://academic.oup.com/ptps/article/doi/10.1143/PTPS.148.284/1881057}
}

@book{GilbargTrudinger2001,
  address = {Berlin, Heidelberg},
  author = {Gilbarg, David and Trudinger, Neil S.},
  doi = {10.1007/978-3-642-61798-0},
  edition = {Second},
  isbn = {978-3-540-41160-4},
  note = {Reprint of the 1998 edition},
  publisher = {Springer},
  series = {Classics in Mathematics},
  title = {Elliptic Partial Differential Equations of Second Order},
  url = {https://link.springer.com/book/10.1007/978-3-642-61798-0},
  year = {2001}
}

@article{GruterWidman1982,
  author = {Gr{\"u}ter, Michael and Widman, Kjell-Ove},
  doi = {10.1007/BF01166225},
  journal = {Manuscripta Mathematica},
  pages = {303--342},
  title = {The {Green} function for uniformly elliptic equations},
  url = {https://link.springer.com/article/10.1007/BF01166225},
  volume = {37},
  year = {1982}
}

@article{Hawking1968,
  author = {Hawking, S. W.},
  doi = {10.1063/1.1664615},
  journal = {Journal of Mathematical Physics},
  pages = {598--604},
  title = {Gravitational radiation in an expanding universe},
  url = {https://doi.org/10.1063/1.1664615},
  volume = {9},
  year = {1968}
}

@misc{Hirsch2023,
  archiveprefix = {arXiv},
  author = {Hirsch, Sven},
  eprint = {2210.12237v3},
  note = {Version 3, 31 December 2023; Conjecture 4.1},
  primaryclass = {math.DG},
  title = {{Hawking} mass monotonicity for initial data sets},
  url = {https://arxiv.org/abs/2210.12237v3},
  year = {2023}
}

@misc{HirschHuang2025,
  archiveprefix = {arXiv},
  author = {Hirsch, Sven and Huang, Lan-Hsuan},
  eprint = {2510.10306v1},
  note = {Version 1, 11 October 2025; Theorems 4 and 7},
  primaryclass = {gr-qc},
  title = {Monotonicity of Causal Killing Vectors and Geometry of {ADM} Mass Minimizers},
  url = {https://arxiv.org/abs/2510.10306v1},
  year = {2025}
}

@article{HirschKazarasKhuri2022,
  archiveprefix = {arXiv},
  author = {Hirsch, Sven and Kazaras, Demetre and Khuri, Marcus},
  doi = {10.4310/jdg/1669998184},
  eprint = {2002.01534},
  journal = {Journal of Differential Geometry},
  number = {2},
  pages = {223--258},
  title = {Spacetime harmonic functions and the mass of 3-dimensional asymptotically flat initial data for the {Einstein} equations},
  url = {https://www.math.stonybrook.edu/~khuri/Hirsch_Kazaras_Khuri.pdf},
  volume = {122},
  year = {2022}
}

@book{HormanderIII,
  address = {Berlin--Heidelberg},
  author = {H{\"o}rmander, Lars},
  doi = {10.1007/978-3-540-49938-1},
  isbn = {9783540499374},
  publisher = {Springer},
  series = {Classics in Mathematics},
  title = {The Analysis of Linear Partial Differential Operators {III}: Pseudo-Differential Operators},
  url = {https://link.springer.com/book/10.1007/978-3-540-49938-1},
  year = {2007}
}

@article{HuangLee2024Bartnik,
  author = {Huang, Lan-Hsuan and Lee, Dan A.},
  title = {{Bartnik} Mass Minimizing Initial Data Sets and Improvability of the Dominant Energy Scalar},
  journal = {Journal of Differential Geometry},
  volume = {126},
  number = {2},
  pages = {741--800},
  year = {2024},
  doi = {10.4310/jdg/1712344222},
  note = {Section numbering agrees with arXiv:2007.00593v2},
  url = {https://arxiv.org/abs/2007.00593v2}
}

@article{HuiskenIlmanen2001,
  author = {Huisken, Gerhard and Ilmanen, Tom},
  doi = {10.4310/jdg/1090349447},
  journal = {Journal of Differential Geometry},
  number = {3},
  pages = {353--437},
  title = {The inverse mean curvature flow and the {Riemannian Penrose} inequality},
  url = {https://doi.org/10.4310/jdg/1090349447},
  volume = {59},
  year = {2001}
}

@article{JangWald1977,
  author = {Jang, Pong Soo and Wald, Robert M.},
  doi = {10.1063/1.523134},
  journal = {Journal of Mathematical Physics},
  number = {1},
  pages = {41--44},
  title = {The positive energy conjecture and the cosmic censor hypothesis},
  url = {https://doi.org/10.1063/1.523134},
  volume = {18},
  year = {1977}
}

@article{KhuriKopinski2023,
  archiveprefix = {arXiv},
  author = {Khuri, Marcus and Kopi{\'n}ski, Jaros{\l}aw},
  doi = {10.1088/1361-6382/acb24b},
  eprint = {2209.01234},
  journal = {Classical and Quantum Gravity},
  number = {4},
  pages = {045007},
  primaryclass = {gr-qc},
  title = {Asymptotically hyperbolic {Einstein} constraint equations with apparent horizon boundary and the {Penrose} inequality for perturbations of {Schwarzschild-AdS}},
  url = {https://doi.org/10.1088/1361-6382/acb24b},
  volume = {40},
  year = {2023}
}

@article{KhuriKunduri2025,
  archiveprefix = {arXiv},
  author = {Khuri, Marcus and Kunduri, Hari},
  doi = {10.4310/ATMP.251120040338},
  eprint = {2404.13247v1},
  journal = {Advances in Theoretical and Mathematical Physics},
  number = {7},
  pages = {1905--1943},
  primaryclass = {math.DG},
  title = {The spacetime {Penrose} inequality for cohomogeneity one initial data},
  url = {https://arxiv.org/abs/2404.13247v1},
  volume = {29},
  year = {2025}
}

@article{KhuriWeinsteinYamada2017,
  archiveprefix = {arXiv},
  author = {Khuri, Marcus and Weinstein, Gilbert and Yamada, Sumio},
  doi = {10.4310/jdg/1500084023},
  eprint = {1409.3271},
  journal = {Journal of Differential Geometry},
  note = {Theorem numbering refers to the linked author manuscript},
  number = {3},
  pages = {451--498},
  title = {Proof of the {Riemannian Penrose} inequality with charge for multiple black holes},
  url = {https://www.math.stonybrook.edu/~khuri/CRPI_Mult_BH.pdf},
  volume = {106},
  year = {2017}
}

@book{LawsonMichelsohn1989,
  address = {Princeton, NJ},
  author = {Lawson, Jr., H. Blaine and Michelsohn, Marie-Louise},
  isbn = {9780691085425},
  publisher = {Princeton University Press},
  series = {Princeton Mathematical Series},
  title = {Spin Geometry},
  url = {https://api.pageplace.de/preview/DT0400.9781400883912_A26852321/preview-9781400883912_A26852321.pdf},
  volume = {38},
  year = {1989}
}

@article{LeraySchauder1934,
  author = {Leray, Jean and Schauder, Jules},
  doi = {10.24033/asens.836},
  journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
  pages = {45--78},
  series = {3},
  title = {Topologie et \'equations fonctionnelles},
  url = {https://www.numdam.org/articles/10.24033/asens.836/},
  volume = {51},
  year = {1934}
}

@article{LesourdUngerYau2021,
  author = {Lesourd, Martin and Unger, Ryan and Yau, Shing-Tung},
  title = {The positive mass theorem with arbitrary ends},
  journal = {Journal of Differential Geometry},
  volume = {128},
  number = {1},
  pages = {257--293},
  year = {2024},
  doi = {10.4310/jdg/1721075263},
  eprint = {2103.02744v1},
  archiveprefix = {arXiv},
  primaryclass = {math.DG},
  url = {https://arxiv.org/abs/2103.02744v1},
  note = {Theorem and definition numbering refers to arXiv:2103.02744v1}
}

@article{LiZhang2022,
  archiveprefix = {arXiv},
  author = {Li, Congming and Zhang, Kai},
  doi = {10.3934/cpaa.2022132},
  eprint = {2110.12967},
  journal = {Communications on Pure and Applied Analysis},
  number = {12},
  pages = {4013--4017},
  primaryclass = {math.AP},
  title = {A note on the {Gagliardo--Nirenberg} inequality in a bounded domain},
  url = {https://arxiv.org/abs/2110.12967},
  volume = {21},
  year = {2022}
}

@article{LittmanStampacchiaWeinberger1963,
  author = {Littman, Walter and Stampacchia, Guido and Weinberger, Hans F.},
  journal = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze},
  number = {1--2},
  pages = {43--77},
  series = {3},
  title = {Regular points for elliptic equations with discontinuous coefficients},
  url = {https://numdam.org/item/ASNSP_1963_3_17_1-2_43_0/},
  volume = {17},
  year = {1963}
}

@book{Maggi2012,
  author = {Maggi, Francesco},
  title = {Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory},
  series = {Cambridge Studies in Advanced Mathematics},
  volume = {135},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  year = {2012},
  doi = {10.1017/CBO9781139108133},
  url = {https://doi.org/10.1017/CBO9781139108133}
}

@article{Mars2009,
  archiveprefix = {arXiv},
  author = {Mars, Marc},
  doi = {10.1088/0264-9381/26/19/193001},
  eprint = {0906.5566},
  journal = {Classical and Quantum Gravity},
  pages = {193001},
  primaryclass = {gr-qc},
  title = {Present status of the {Penrose} inequality},
  url = {https://arxiv.org/abs/0906.5566},
  volume = {26},
  year = {2009}
}

@article{MichaelSimon1973,
  author = {Michael, J. H. and Simon, L. M.},
  doi = {10.1002/cpa.3160260305},
  journal = {Communications on Pure and Applied Mathematics},
  number = {3},
  pages = {361--379},
  title = {{Sobolev} and mean-value inequalities on generalized submanifolds of {$\mathbb{R}^{n}$}},
  url = {https://onlinelibrary.wiley.com/doi/10.1002/cpa.3160260305},
  volume = {26},
  year = {1973}
}

@article{Nash1956,
  author = {Nash, John},
  doi = {10.2307/1969989},
  journal = {Annals of Mathematics},
  number = {1},
  pages = {20--63},
  series = {2},
  title = {The imbedding problem for {Riemannian} manifolds},
  url = {https://www.jstor.org/stable/1969989},
  volume = {63},
  year = {1956}
}

@article{NevesTian2009,
  archiveprefix = {arXiv},
  author = {Neves, Andr{\'e} and Tian, Gang},
  doi = {10.1007/s00039-009-0019-1},
  eprint = {math/0610767},
  journal = {Geometric and Functional Analysis},
  number = {3},
  pages = {910--942},
  primaryclass = {math.DG},
  title = {Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds},
  url = {https://doi.org/10.1007/s00039-009-0019-1},
  volume = {19},
  year = {2009}
}

@article{Nirenberg1959,
  author = {Nirenberg, Louis},
  journal = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze},
  number = {2},
  pages = {115--162},
  series = {3},
  title = {On elliptic partial differential equations},
  url = {https://numdam.org/item/ASNSP_1959_3_13_2_115_0/},
  volume = {13},
  year = {1959}
}

@book{ONeill1983,
  address = {New York},
  author = {O'Neill, Barrett},
  isbn = {9780125267403},
  publisher = {Academic Press},
  series = {Pure and Applied Mathematics},
  title = {Semi-{Riemannian} Geometry with Applications to Relativity},
  url = {https://shop.elsevier.com/books/semi-riemannian-geometry-with-applications-to-relativity/oneill/978-0-12-526740-3},
  volume = {103},
  year = {1983}
}

@article{Penrose1973,
  author = {Penrose, Roger},
  doi = {10.1111/j.1749-6632.1973.tb41447.x},
  journal = {Annals of the New York Academy of Sciences},
  month = {December},
  number = {1},
  pages = {125--134},
  title = {Naked singularities},
  url = {https://doi.org/10.1111/j.1749-6632.1973.tb41447.x},
  volume = {224},
  year = {1973}
}

@book{Petersen2016,
  author = {Petersen, Peter},
  title = {{Riemannian} Geometry},
  edition = {Third},
  series = {Graduate Texts in Mathematics},
  volume = {171},
  publisher = {Springer},
  address = {Cham},
  year = {2016},
  doi = {10.1007/978-3-319-26654-1},
  url = {https://doi.org/10.1007/978-3-319-26654-1}
}

@book{RudinFA1991,
  address = {New York},
  author = {Rudin, Walter},
  edition = {Second},
  isbn = {0070542368},
  publisher = {McGraw-Hill},
  series = {International Series in Pure and Applied Mathematics},
  title = {Functional Analysis},
  year = {1991}
}

@book{RudinRCA1987,
  address = {New York},
  author = {Rudin, Walter},
  edition = {Third},
  isbn = {0070542341},
  publisher = {McGraw-Hill},
  title = {Real and Complex Analysis},
  year = {1987}
}

@book{Simon1983,
  address = {Canberra},
  author = {Simon, Leon},
  publisher = {Centre for Mathematical Analysis, Australian National University},
  series = {Proceedings of the Centre for Mathematical Analysis, Australian National University},
  title = {Lectures on Geometric Measure Theory},
  url = {https://maths.anu.edu.au/files/CMAProcVol3-Complete_1.pdf},
  volume = {3},
  year = {1983}
}

@misc{Simon2014,
  author = {Simon, Leon},
  howpublished = {Stanford University lecture notes for the Tsinghua lectures},
  note = {Author's notes: \url{https://web.stanford.edu/class/math285/ts-gmt.pdf}},
  title = {Introduction to Geometric Measure Theory},
  url = {https://web.stanford.edu/class/math285/ts-gmt.pdf},
  year = {2014}
}

@article{Spector2011,
  author = {Spector, Daniel},
  title = {Simple Proofs of Some Results of {Reshetnyak}},
  journal = {Proceedings of the American Mathematical Society},
  volume = {139},
  number = {5},
  pages = {1681--1690},
  year = {2011},
  doi = {10.1090/S0002-9939-2010-10593-2},
  note = {Theorem numbering refers to the author manuscript revised 18 May 2010},
  url = {https://cvgmt.sns.it/media/doc/paper/505/reshetnyakcontinuityrevised.pdf}
}

@article{Talenti1965,
  author = {Talenti, Giorgio},
  doi = {10.1007/BF02414375},
  journal = {Annali di Matematica Pura ed Applicata},
  pages = {285--304},
  series = {4},
  title = {Sopra una classe di equazioni ellittiche a coefficienti misurabili},
  url = {https://link.springer.com/article/10.1007/BF02414375},
  volume = {69},
  year = {1965}
}

@article{Tangherlini1963,
  author = {Tangherlini, F. R.},
  doi = {10.1007/BF02784569},
  journal = {Il Nuovo Cimento},
  pages = {636--651},
  title = {{Schwarzschild} field in {$n$} dimensions and the dimensionality of space problem},
  url = {https://link.springer.com/article/10.1007/BF02784569},
  volume = {27},
  year = {1963}
}

@article{Wallace1960,
  author = {Wallace, Andrew H.},
  doi = {10.4153/CJM-1960-045-7},
  journal = {Canadian Journal of Mathematics},
  pages = {503--528},
  title = {Modifications and cobounding manifolds},
  url = {https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/modifications-and-cobounding-manifolds/F57667117001CFAA8455ACB0753F4530},
  volume = {12},
  year = {1960}
}

@article{WeinsteinYamada2005,
  archiveprefix = {arXiv},
  author = {Weinstein, Gilbert and Yamada, Sumio},
  doi = {10.1007/s00220-005-1355-0},
  eprint = {math/0405602},
  journal = {Communications in Mathematical Physics},
  number = {3},
  pages = {703--723},
  title = {On a {Penrose} inequality with charge},
  url = {https://arxiv.org/abs/math/0405602},
  volume = {257},
  year = {2005}
}

@article{White1999,
  author = {White, Brian},
  doi = {10.1007/BF02392829},
  journal = {Acta Mathematica},
  number = {2},
  pages = {255--271},
  title = {The deformation theorem for flat chains},
  url = {https://link.springer.com/article/10.1007/BF02392829},
  volume = {183},
  year = {1999}
}

@article{Witten1981,
  author = {Witten, Edward},
  doi = {10.1007/BF01208277},
  journal = {Communications in Mathematical Physics},
  number = {3},
  pages = {381--402},
  title = {A new proof of the positive energy theorem},
  url = {https://www.ias.edu/sites/default/files/sns/%5B32%5DCMP_80_1981.pdf},
  volume = {80},
  year = {1981}
}

@misc{ChargedOriginalData2026,
  author = {{OpenAI}},
  title = {{The spacetime Penrose inequality with charge and original-data rigidity}},
  howpublished = {OpenAI Math Release preprint
    \href{https://github.com/openai/math/blob/main/preprints/The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026/paper.pdf}{OAI:The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026}},
  year = {2026}
}
