@incollection{Yau1982,
  author    = {Yau, Shing-Tung},
  title     = {Problem section},
  booktitle = {Seminar on Differential Geometry},
  editor    = {Yau, Shing-Tung},
  series    = {Annals of Mathematics Studies},
  volume    = {102},
  publisher = {Princeton University Press},
  address   = {Princeton, NJ},
  year      = {1982},
  pages     = {669--706},
  doi       = {10.1515/9781400881918-035},
  url       = {https://doi.org/10.1515/9781400881918-035}
}

@article{DonnellyFefferman1988,
  author  = {Donnelly, Harold and Fefferman, Charles},
  title   = {Nodal sets of eigenfunctions on {Riemannian} manifolds},
  journal = {Inventiones Mathematicae},
  volume  = {93},
  number  = {1},
  year    = {1988},
  pages   = {161--183},
  doi     = {10.1007/BF01393691},
  url     = {https://doi.org/10.1007/BF01393691}
}

@article{LogunovUpper2018,
  author  = {Logunov, Alexander},
  title   = {Nodal sets of {Laplace} eigenfunctions: polynomial upper estimates of the {Hausdorff} measure},
  journal = {Annals of Mathematics (2)},
  volume  = {187},
  number  = {1},
  year    = {2018},
  pages   = {221--239},
  doi     = {10.4007/annals.2018.187.1.4},
  url     = {https://annals.math.princeton.edu/2018/187-1/p04}
}

@article{LogunovLower2018,
  author  = {Logunov, Alexander},
  title   = {Nodal sets of {Laplace} eigenfunctions: proof of {Nadirashvili}'s conjecture and of the lower bound in {Yau}'s conjecture},
  journal = {Annals of Mathematics (2)},
  volume  = {187},
  number  = {1},
  year    = {2018},
  pages   = {241--262},
  doi     = {10.4007/annals.2018.187.1.5},
  url     = {https://annals.math.princeton.edu/2018/187-1/p05}
}

@article{Hezari2023,
  author  = {Hezari, Hamid},
  title   = {Upper bounds on the size of nodal sets for {Gevrey} and quasianalytic {Riemannian} manifolds},
  journal = {Communications in Mathematical Physics},
  volume  = {404},
  number  = {3},
  pages   = {1341--1359},
  year    = {2023},
  doi     = {10.1007/s00220-023-04853-z},
  url     = {https://doi.org/10.1007/s00220-023-04853-z}
}

@article{EncisoPeraltaSalas2015,
  author  = {Enciso, Alberto and Peralta-Salas, Daniel},
  title   = {Eigenfunctions with prescribed nodal sets},
  journal = {Journal of Differential Geometry},
  volume  = {101},
  number  = {2},
  pages   = {197--211},
  year    = {2015},
  doi     = {10.4310/jdg/1442364650},
  url     = {https://doi.org/10.4310/jdg/1442364650}
}

@incollection{EncisoPeraltaSalasTorres2018,
  author    = {Enciso, Alberto and Peralta-Salas, Daniel and Torres de Lizaur, Francisco},
  title     = {High-energy eigenfunctions of the {Laplacian} on the torus and the sphere with nodal sets of complicated topology},
  booktitle = {Nonlinear Partial Differential Equations for Future Applications},
  editor    = {Koike, Shigeaki and Kozono, Hideo and Ogawa, Takayoshi and Sakaguchi, Shigeru},
  series    = {Springer Proceedings in Mathematics \& Statistics},
  volume    = {346},
  publisher = {Springer},
  address   = {Singapore},
  year      = {2021},
  pages     = {245--261},
  doi       = {10.1007/978-981-33-4822-6_7},
  url       = {https://arxiv.org/abs/1810.09277v1}
}

@article{Aronszajn1957,
  author  = {Aronszajn, N.},
  title   = {A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order},
  journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es (9)},
  volume  = {36},
  year    = {1957},
  pages   = {235--249},
  url     = {https://sites.math.washington.edu/~blwilson/Nodal/Aronszajn.pdf}
}

@article{DenckerSjostrandZworski2004,
  author  = {Dencker, Nils and Sj{\"o}strand, Johannes and Zworski, Maciej},
  title   = {Pseudospectra of semiclassical {\mbox{(pseudo-)}} differential operators},
  journal = {Communications on Pure and Applied Mathematics},
  volume  = {57},
  number  = {3},
  year    = {2004},
  pages   = {384--415},
  doi     = {10.1002/cpa.20004},
  url     = {https://arxiv.org/abs/math/0301242v1},
  note    = {Section locators follow arXiv:math/0301242v1}
}

@article{CharalambousLu2015,
  author  = {Charalambous, Nelia and Lu, Zhiqin},
  title   = {Heat kernel estimates and the essential spectrum on weighted manifolds},
  journal = {Journal of Geometric Analysis},
  volume  = {25},
  year    = {2015},
  pages   = {536--563},
  doi     = {10.1007/s12220-013-9438-1},
  url     = {https://doi.org/10.1007/s12220-013-9438-1}
}

@book{Evans2010,
  author    = {Evans, Lawrence C.},
  title     = {Partial Differential Equations},
  edition   = {Second},
  series    = {Graduate Studies in Mathematics},
  volume    = {19},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  year      = {2010},
  url       = {https://bookstore.ams.org/gsm-19-r}
}

@misc{OpenAINodalQualitative2026,
  author = {{OpenAI}},
  title = {{Smooth counterexamples to Yau's nodal upper bound in dimensions three and four}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026/paper.pdf}{OAI:Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026}},
  year = {2026}
}