Sharp Steklov upper bound for submanifolds of revolution

TL;DR

This paper establishes a precise upper limit for the Steklov spectrum on a specific class of revolution submanifolds in Euclidean space, enhancing understanding of spectral geometry in these contexts.

Contribution

It provides the first sharp upper bound for the Steklov spectrum on submanifolds of revolution with a single boundary component.

Findings

Derived a sharp upper bound for the Steklov spectrum.

Applied the bound specifically to submanifolds of revolution.

Enhanced spectral geometry understanding for these submanifolds.

Abstract

In this note, we find a sharp upper bound for the Steklov spectrum on a submanifold of revolution in Euclidean space with one boundary component.