Reilly-type upper bounds for the $p$-Steklov problem on submanifolds

TL;DR

This paper establishes Reilly-type upper bounds for the first non-zero eigenvalue of the $p$-Steklov problem on submanifolds within manifolds having bounded sectional curvature, extending classical spectral estimates.

Contribution

It introduces new upper bounds for the $p$-Steklov eigenvalues on submanifolds, generalizing previous results to the $p$-Laplace setting under curvature constraints.

Findings

Derived Reilly-type upper bounds for the $p$-Steklov eigenvalues.

Extended classical eigenvalue estimates to the $p$-Laplace operator.

Applicable to submanifolds in manifolds with non-negative sectional curvature.

Abstract

We prove Reilly-type upper bounds for the first non-zero eigenvalue of the Steklov problem associated with the $p$-Laplace operator on submanifolds of manifolds with sectional curvature bounded form above by a non-negative constant.