A symmetry condition for genus zero free boundary minimal surfaces attaining the first eigenvalue of one

2024/09/23 by Dong-Hwi Seo, Seo, Dong-Hwi
Mathematics · #53A10 #58C40 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2409.14718

openalex publication_date 2024/09/23 · openalex created_date 2024/10/26 · openalex updated_date 2026/07/28

Abstract

An embedded free boundary minimal surface in the 3-ball has a Steklov eigenvalue of one due to its coordinate functions. Fraser and Li conjectured that whether one is the first nonzero Steklov eigenvalue. In this paper, we show that if an embedded free boundary minimal surface of genus zero, with n boundary components, in the 3-ball has n distinct reflection planes, then one is the first eigenvalue of the surface.

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