@article{Aubin1976,
  author = {Aubin, Thierry},
  title = {Probl{\`e}mes isop{\'e}rim{\'e}triques et espaces de {Sobolev}},
  journal = {Journal of Differential Geometry},
  volume = {11},
  number = {4},
  year = {1976},
  pages = {573--598},
  doi = {10.4310/jdg/1214433725},
  note = {\url{https://doi.org/10.4310/jdg/1214433725}}
}

@article{Bol1941,
  author = {Bol, Gerrit},
  title = {{Isoperimetrische Ungleichungen f{\"u}r Bereiche auf Fl{\"a}chen}},
  journal = {Jahresbericht der Deutschen Mathematiker-Vereinigung},
  volume = {51},
  year = {1941},
  pages = {219--257},
  url = {https://eudml.org/doc/146284},
  note = {\url{https://eudml.org/doc/146284}}
}

@article{BrezisLieb1983,
  author = {Brezis, Ha{\"i}m and Lieb, Elliott},
  title = {A relation between pointwise convergence of functions and convergence of functionals},
  journal = {Proceedings of the American Mathematical Society},
  volume = {88},
  number = {3},
  year = {1983},
  pages = {486--490},
  doi = {10.1090/S0002-9939-1983-0699419-3},
  note = {\url{https://doi.org/10.1090/S0002-9939-1983-0699419-3}}
}

@article{Croke1984,
  author = {Croke, Christopher B.},
  title = {A sharp four dimensional isoperimetric inequality},
  journal = {Commentarii Mathematici Helvetici},
  volume = {59},
  year = {1984},
  pages = {187--192},
  doi = {10.1007/BF02566344},
  note = {\url{https://doi.org/10.1007/BF02566344}}
}

@misc{Ghomi2026Pinched,
  author = {Ghomi, Mohammad},
  title = {Total curvature and isoperimetric inequalities in pinched {Cartan--Hadamard} manifolds},
  year = {2026},
  eprint = {2608.12020},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  howpublished = {arXiv:2608.12020v1},
  note = {\url{https://arxiv.org/abs/2608.12020v1}}
}

@article{GhomiSpruck2022,
  author = {Ghomi, Mohammad and Spruck, Joel},
  title = {Total curvature and the isoperimetric inequality in {Cartan--Hadamard} manifolds},
  journal = {Journal of Geometric Analysis},
  volume = {32},
  year = {2022},
  pages = {Paper No.~50, 54 pp.},
  doi = {10.1007/s12220-021-00801-2},
  eprint = {1908.09814},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  note = {Also available as \href{https://arxiv.org/abs/1908.09814v7}{arXiv:1908.09814v7}},
  url = {https://arxiv.org/abs/1908.09814v7}
}

@article{GhomiStavroulakis2026,
  author = {Ghomi, Mohammad and Stavroulakis, John Ioannis},
  title = {A local isoperimetric inequality for balls with nonpositive curvature},
  journal = {International Mathematics Research Notices},
  volume = {2026},
  number = {6},
  year = {2026},
  pages = {rnag043},
  doi = {10.1093/imrn/rnag043},
  note = {\url{https://doi.org/10.1093/imrn/rnag043}}
}

@article{Kleiner1992,
  author = {Kleiner, Bruce},
  title = {An isoperimetric comparison theorem},
  journal = {Inventiones Mathematicae},
  volume = {108},
  year = {1992},
  pages = {37--47},
  doi = {10.1007/BF02100598},
  note = {\url{https://doi.org/10.1007/BF02100598}}
}

@article{KloecknerKuperberg2019,
  author = {Kloeckner, Beno{\^i}t R. and Kuperberg, Greg},
  title = {The {Cartan--Hadamard} conjecture and the {Little Prince}},
  journal = {Revista Matem{\'a}tica Iberoamericana},
  volume = {35},
  number = {4},
  year = {2019},
  pages = {1195--1258},
  doi = {10.4171/RMI/1082},
  eprint = {1303.3115},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  url = {https://ems.press/journals/rmi/articles/16336},
  note = {Theorem numbering refers to \href{https://arxiv.org/abs/1303.3115v3}{arXiv:1303.3115v3}; \url{https://doi.org/10.4171/RMI/1082}}
}

@article{LiYau1982,
  author = {Li, Peter and Yau, Shing-Tung},
  title = {A new conformal invariant and its applications to the {Willmore} conjecture and the first eigenvalue of compact surfaces},
  journal = {Inventiones Mathematicae},
  volume = {69},
  number = {2},
  year = {1982},
  pages = {269--291},
  doi = {10.1007/BF01399507},
  note = {\url{https://doi.org/10.1007/BF01399507}},
  url = {https://math.jhu.edu/~js/Math748/li-yau.conformal.pdf}
}

@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},
  year = {2012},
  doi = {10.1017/CBO9781139108133},
  isbn = {9781107021037},
  url = {https://doi.org/10.1017/CBO9781139108133},
  note = {\url{https://doi.org/10.1017/CBO9781139108133}; author extract, including the Synopsis: \url{https://web.ma.utexas.edu/users/maggi/Maggi_extract.pdf}}
}

@article{Morgan2003,
  author = {Morgan, Frank},
  title = {Regularity of isoperimetric hypersurfaces in {Riemannian} manifolds},
  journal = {Transactions of the American Mathematical Society},
  volume = {355},
  number = {12},
  year = {2003},
  pages = {5041--5052},
  doi = {10.1090/S0002-9947-03-03061-7},
  url = {https://doi.org/10.1090/S0002-9947-03-03061-7},
  note = {\url{https://doi.org/10.1090/S0002-9947-03-03061-7}}
}

@misc{PetersenManuscript,
  author = {Petersen, Peter},
  title = {{Riemannian} Geometry},
  howpublished = {Author-hosted manuscript, \url{https://www.math.ucla.edu/~petersen/RG.pdf}},
  note = {Undated manuscript, accessed 23 September 2026; manuscript theorem and page numbers are used},
  url = {https://www.math.ucla.edu/~petersen/RG.pdf}
}

@article{Talenti1976,
  author = {Talenti, Giorgio},
  title = {Best constant in {Sobolev} inequality},
  journal = {Annali di Matematica Pura ed Applicata},
  volume = {110},
  year = {1976},
  pages = {353--372},
  doi = {10.1007/BF02418013},
  note = {\url{https://doi.org/10.1007/BF02418013}}
}

@article{Weil1926,
  author = {Weil, Andr{\'e}},
  title = {Sur les surfaces {\`a} courbure n{\'e}gative},
  journal = {Comptes rendus hebdomadaires des s{\'e}ances de l'Acad{\'e}mie des sciences},
  volume = {182},
  year = {1926},
  pages = {1069--1071}
}


@article{ChavelFeldman1980,
  author = {Chavel, Isaac and Feldman, Edgar A.},
  title = {Isoperimetric inequalities on curved surfaces},
  journal = {Advances in Mathematics},
  volume = {37},
  number = {2},
  year = {1980},
  pages = {83--98},
  doi = {10.1016/0001-8708(80)90028-6},
  note = {\url{https://doi.org/10.1016/0001-8708(80)90028-6}}
}

@article{GuneysuPallara2015,
  author = {G{\"u}neysu, Batu and Pallara, Diego},
  title = {Functions with bounded variation on a class of {Riemannian} manifolds with {Ricci} curvature unbounded from below},
  journal = {Mathematische Annalen},
  volume = {363},
  year = {2015},
  pages = {1307--1331},
  doi = {10.1007/s00208-015-1208-x},
  note = {Author's final preprint, \url{https://cvgmt.sns.it/media/doc/paper/2044/BVfunctionsfinal.pdf}; preprint theorem numbering is used}
}

@article{AntonelliPasqualettoPozzetta2022,
  author = {Antonelli, Gioacchino and Pasqualetto, Enrico and Pozzetta, Marco},
  title = {Isoperimetric sets in spaces with lower bounds on the {Ricci} curvature},
  journal = {Nonlinear Analysis},
  volume = {220},
  year = {2022},
  pages = {112839},
  doi = {10.1016/j.na.2022.112839},
  eprint = {2107.03124},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  note = {Theorem numbering refers to \href{https://arxiv.org/abs/2107.03124v2}{arXiv:2107.03124v2}},
  url = {https://arxiv.org/abs/2107.03124v2}
}

@misc{ChenGhomiWang2026HigherDimensions,
  author = {Chen, Shibing and Ghomi, Mohammad and Wang, Peng},
  title = {The isoperimetric inequality and {CMC} hypersurfaces in {Cartan--Hadamard} manifolds},
  year = {2026},
  eprint = {2609.20517},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  howpublished = {Preprint, arXiv:2609.20517v1},
  note = {Submitted 17 September 2026; \url{https://arxiv.org/abs/2609.20517v1}},
  url = {https://arxiv.org/abs/2609.20517v1}
}

@misc{AgnolettoDaSilvaNardulliResende2026,
  author = {Agnoletto, Marcos and {Da Silva}, M{\'a}rcio Fabiano and Nardulli, Stefano and Resende, Reinaldo},
  title = {A proof of the {Cartan--Hadamard} conjecture for small volumes under a {Ricci} curvature lower bound},
  year = {2026},
  eprint = {2609.17093},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  note = {arXiv:2609.17093v2, revised 21 September 2026; \url{https://arxiv.org/abs/2609.17093v2}},
  url = {https://arxiv.org/abs/2609.17093v2}
}

@misc{Wheeler2026,
  author = {Wheeler, Glen},
  title = {The {Cartan--Hadamard} isoperimetric inequality under controlled variation of curvature},
  year = {2026},
  eprint = {2609.14505},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  note = {arXiv:2609.14505v1, 13 September 2026; \url{https://arxiv.org/abs/2609.14505v1}},
  url = {https://arxiv.org/abs/2609.14505v1}
}

@article{BeckenbachRado1933,
  author = {Beckenbach, Edwin F. and Rad{\'o}, Tibor},
  title = {Subharmonic functions and surfaces of negative curvature},
  journal = {Transactions of the American Mathematical Society},
  volume = {35},
  number = {3},
  year = {1933},
  pages = {662--674},
  doi = {10.1090/S0002-9947-1933-1501708-X},
  note = {\url{https://doi.org/10.1090/S0002-9947-1933-1501708-X}}
}

@article{StredulinskyZiemer1997,
  author = {Stredulinsky, Edward and Ziemer, William P.},
  title = {Area minimizing sets subject to a volume constraint in a convex set},
  journal = {Journal of Geometric Analysis},
  volume = {7},
  number = {4},
  year = {1997},
  pages = {653--677},
  doi = {10.1007/BF02921639},
  note = {\url{https://doi.org/10.1007/BF02921639}}
}

@article{NobiliViolo2025,
  author = {Nobili, Francesco and Violo, Ivan Yuri},
  title = {Fine {P{\'o}lya--Szeg{\H{o}}} rearrangement inequalities in metric spaces and applications},
  journal = {Calculus of Variations and Partial Differential Equations},
  volume = {64},
  year = {2025},
  pages = {Paper No.~276},
  doi = {10.1007/s00526-025-03155-7},
  eprint = {2409.14182},
  archivePrefix = {arXiv},
  primaryClass = {math.AP},
  note = {Theorem numbering refers to \href{https://arxiv.org/abs/2409.14182v2}{arXiv:2409.14182v2}; \url{https://doi.org/10.1007/s00526-025-03155-7}},
  url = {https://arxiv.org/abs/2409.14182v2}
}

@article{BrianiButtazzoPrinari2022,
  author = {Briani, Luca and Buttazzo, Giuseppe and Prinari, Francesca},
  title = {Inequalities between torsional rigidity and principal eigenvalue of the {$p$-Laplacian}},
  journal = {Calculus of Variations and Partial Differential Equations},
  volume = {61},
  year = {2022},
  pages = {Paper No.~78},
  doi = {10.1007/s00526-021-02129-9},
  note = {\url{https://doi.org/10.1007/s00526-021-02129-9}}
}

@article{AntonelliBrueFogagnoloPozzetta2022,
  author = {Antonelli, Gioacchino and Bru{\`e}, Elia and Fogagnolo, Mattia and Pozzetta, Marco},
  title = {On the existence of isoperimetric regions in manifolds with nonnegative {Ricci} curvature and {Euclidean} volume growth},
  journal = {Calculus of Variations and Partial Differential Equations},
  volume = {61},
  year = {2022},
  pages = {Paper No.~77},
  doi = {10.1007/s00526-022-02193-9},
  note = {\url{https://doi.org/10.1007/s00526-022-02193-9}}
}