A Payne-Weinberger eigenvalue estimate for wedge domains on spheres

TL;DR

This paper extends eigenvalue estimates to wedge domains on spheres, providing sharp bounds for the first Dirichlet eigenvalue and applying these results to Brownian motion capture time analysis.

Contribution

It generalizes Payne-Weinberger eigenvalue bounds from the plane to spherical wedge domains, offering a new proof for Brownian motion capture time finiteness.

Findings

Sharp lower bound for first Dirichlet eigenvalue on spherical wedges

Extension of Payne-Weinberger inequality to spherical geometry

Alternative proof for Brownian motion capture time finiteness

Abstract

A Faber-Krahn type argument gives a sharp lower estimate for the first Dirichlet eigenvalue for subdomains of wedge domains in spheres, generalizing the inequality in the plane, found by Payne and Weinberger. An application is an alternative proof to the finiteness of a Brownian motion capture time estimate.