Sharp Bounds for Eigenvalues and Multiplicities on Surfaces of Revolution

TL;DR

This paper establishes precise upper bounds for the eigenvalues and their multiplicities on surfaces of revolution that are topologically equivalent to a sphere, advancing understanding of spectral properties of such geometric objects.

Contribution

It provides new sharp bounds for eigenvalues and multiplicities on surfaces of revolution, a specific class of geometric surfaces.

Findings

Sharp upper bounds for eigenvalues.

Sharp bounds for eigenvalue multiplicities.

Applicable to surfaces diffeomorphic to the sphere.

Abstract

We find sharp upper bounds for the multiplicities and the numerical values of all the distinct eigenvalues on a surface of revolution diffeomorphic to the sphere.