Compact bordered Riemannian surfaces as vibrating membranes: an estimate \`a la Hersch-Yang-Yau-Fraser-Schoen

TL;DR

This paper establishes an estimate connecting the first Dirichlet and Neumann eigenvalues of compact bordered Riemannian surfaces, contributing to the spectral geometry understanding of these surfaces.

Contribution

It introduces a new estimate relating eigenvalues of bordered Riemannian surfaces, extending classical spectral bounds to this setting.

Findings

Derived a new eigenvalue estimate for bordered Riemannian surfaces

Extended classical spectral bounds to surfaces with boundary

Provided insights into the vibrational properties of membranes

Abstract

We try to present an estimate relating the first Dirichlet and Neumann eigenvalues of a compact bordered Riemannian surface.