The first Steklov eigenvalue on manifolds with nonnegative Ricci curvature and convex boundary

TL;DR

This paper derives a new lower bound for the first Steklov eigenvalue on compact Riemannian manifolds with non-negative Ricci curvature and convex boundary, extending to weaker geometric conditions.

Contribution

It provides a novel lower bound for the first Steklov eigenvalue under specific curvature and boundary convexity assumptions, with extensions to weaker conditions.

Findings

Established a new lower bound for the Steklov eigenvalue.

Extended results to manifolds with weaker geometric hypotheses.

Enhanced understanding of spectral geometry under curvature constraints.

Abstract

We establish a new lower bound for the first non-zero Steklov eigenvalue of a compact Riemannian manifold with non-negative Ricci curvature and (strictly) convex boundary. Related results are also obtained under weaker geometric hypotheses.