On Berger’s isoperimetric problem

Fan Kang

doi:10.5802/crmath.749

Research article - Geometry and Topology, Spectral theory

On Berger’s isoperimetric problem

Fan Kang ¹

¹ School of Mathematical Sciences, Capital Normal University, 100048, Beijing, China

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 695-704

Abstract (Original language)
Résumé

Berger’s isoperimetric problem asks if the flat equilateral torus is $\lambda _1$-maximal. In 1996, Nadirashvili first gave a positive answer. In this paper, we use El Soufi–Ilias–Ros’s method in [8] and Bryant’s result in [3] to give a new proof.

Le problème isopérimétrique de Berger demande si le tore plat équilatéral est $\lambda _1$-maximal. En 1996, Nadirashvili a donné pour la première fois une réponse positive. Dans cet article, nous utilisons la méthode d’El Soufi–Ilias–Ros dans [8] et le résultat de Bryant dans [3] pour donner une nouvelle preuve.

Received: 2024-05-23
Revised: 2025-03-23
Accepted: 2025-04-09
Published online: 2025-06-23

DOI: 10.5802/crmath.749

Author's affiliations:

Fan Kang ¹

¹ School of Mathematical Sciences, Capital Normal University, 100048, Beijing, China

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Fan Kang},
     title = {On {Berger{\textquoteright}s} isoperimetric problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {695--704},
     year = {2025},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     doi = {10.5802/crmath.749},
     language = {en},
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Fan Kang. On Berger’s isoperimetric problem. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 695-704. doi: 10.5802/crmath.749

References
Cited by

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