no. 1
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]

Présenté par : the Editorial Board

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.

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.

Reçu le :
Accepté le :
Publié le :
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://www.numdam.org/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.