Fundamental gaps of spherical triangles

2020/09/01 by Shoo Seto, Seto, Shoo, Guofang Wei +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2009.00229

openalex publication_date 2020/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute Dirichlet eigenvalues and eigenfunctions explicitly for spherical lunes and the spherical triangles which are half the lunes, and show that the fundamental gap goes to infinity when the angle of the lune goes to zero. Then we show the spherical equilateral triangle of diameter \fracπ2 is a strict local minimizer of the fundamental gap on the space of the spherical triangles with diameter \fracπ2, which partially extends Lu-Rowlett's result from the plane to the sphere.

Cited by

• Dirichlet eigenvalues of Schwarz triangle (3/2 3/2 3/2)

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