English

On Berger's Isoperimetric Problem

Differential Geometry 2025-06-09 v1 Spectral Theory

Abstract

Berger's isoperimetric problem asks if the flat equilateral torus is λ1\lambda_1-maximal. In 1996, Nadirashvili first gave a positive answer. In this paper, we use El Soufi-Ilias-Ros's method and Bryant's result (arXiv:1507.01485) to give a new proof.

Cite

@article{arxiv.2506.05775,
  title  = {On Berger's Isoperimetric Problem},
  author = {Fan Kang},
  journal= {arXiv preprint arXiv:2506.05775},
  year   = {2025}
}

Comments

to appear in Comptes Rendus Math\'ematique

R2 v1 2026-07-01T03:03:02.378Z