Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian

2017/04/21 by Shin Nayatani, Nayatani, Shin, Toshihiro Shoda +1 · 3 citations
Mathematics · #53A10 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1704.06384

openalex publication_date 2017/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• On Berger's Isoperimetric Problem
• An improved upper bound for the second eigenvalue on tori
• First-eigenvalue maximization and inflation of maps

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