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

TL;DR

This paper calculates the first two Dirichlet eigenvalues and eigenfunctions for the equilateral Schwarz triangle on the sphere, providing insights into its spectral properties.

Contribution

It offers the first explicit computation of eigenvalues and eigenfunctions for this specific spherical triangle, advancing spectral geometry knowledge.

Findings

First two Dirichlet eigenvalues computed

Eigenfunctions explicitly determined

Enhanced understanding of spherical triangle spectra

Abstract

In this paper we compute the first two Dirichlet eigenvalues and corresponding eigenfunctions of the equilateral Schwarz triangle (3/2 3/2 3/2) on the sphere.