In this paper, we settle in the affirmative the Jakobson–Levitin–Nadirashvili–Nigam–Polterovich conjecture, stating that a certain singular metric on the Bolza surface, with area normalized, should maximize the first eigenvalue of the Laplacian.
Dans cette Note, nous donnons une réponse positive à la conjecture de Jakobson–Levitin–Nadirashvili–Nigam–Polterovich, en montrant qu'une certaine métrique singulière sur la surface de Bolza, d'aire normalisée, maximise la première valeur propre du laplacien.
Accepted:
Published online:
Shin Nayatani 1; Toshihiro Shoda 2
@article{CRMATH_2019__357_1_84_0, author = {Shin Nayatani and Toshihiro Shoda}, title = {Metrics on a closed surface of genus two which maximize the first eigenvalue of the {Laplacian}}, journal = {Comptes Rendus. Math\'ematique}, pages = {84--98}, publisher = {Elsevier}, volume = {357}, number = {1}, year = {2019}, doi = {10.1016/j.crma.2018.11.008}, language = {en}, }
TY - JOUR AU - Shin Nayatani AU - Toshihiro Shoda TI - Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian JO - Comptes Rendus. Mathématique PY - 2019 SP - 84 EP - 98 VL - 357 IS - 1 PB - Elsevier DO - 10.1016/j.crma.2018.11.008 LA - en ID - CRMATH_2019__357_1_84_0 ER -
Shin Nayatani; Toshihiro Shoda. Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian. Comptes Rendus. Mathématique, Volume 357 (2019) no. 1, pp. 84-98. doi : 10.1016/j.crma.2018.11.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.11.008/
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☆ This work was supported by the Research Institute for Mathematical Sciences, a Joint Usage/Research Center located in Kyoto University.
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