Geodesic
Differential geometry
Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian
[Métriques sur une surface fermée de genre deux qui maximisent la première valeur propre du laplacien]

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Nayatani, Shin1 ; Shoda, Toshihiro2
1 Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
2 Faculty of Education, Saga University, Honjo-machi, Saga 840-8502, Japan
Comptes Rendus. Mathématique, Tome 357 (2019) no. 1, pp. 84-98.

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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.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2018.11.008

Nayatani, Shin 1 ; Shoda, Toshihiro 2

1 Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
2 Faculty of Education, Saga University, Honjo-machi, Saga 840-8502, Japan 
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Nayatani, Shin; Shoda, Toshihiro. Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian. Comptes Rendus. Mathématique, Tome 357 (2019) no. 1, pp. 84-98. doi : 10.1016/j.crma.2018.11.008. http://geodesic.mathdoc.fr/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.