Upper bounds for Steklov eigenvalues of a hypersurface of revolution

TL;DR

This paper establishes upper bounds for the first Steklov eigenvalue on surfaces of revolution with two spherical boundaries of different radii, and identifies cases where these bounds are sharp.

Contribution

It provides new upper bounds for Steklov eigenvalues on specific hypersurfaces of revolution and characterizes cases of equality.

Findings

Derived upper bounds for the first Steklov eigenvalue.

Identified conditions under which the bounds are sharp.

Enhanced understanding of spectral properties of revolution surfaces.

Abstract

In this paper we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that in some cases this boundary is sharp.