[Métriques sur une surface fermée de genre deux qui maximisent la première valeur propre du laplacien]
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.
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.
Accepté le :
Publié le :
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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