First eigenvalue of the $p$-Laplacian under integral curvature condition

TL;DR

This paper provides estimates for the first eigenvalue of the p-Laplacian on closed Riemannian manifolds under integral curvature conditions, advancing understanding of geometric analysis in this context.

Contribution

It introduces new eigenvalue estimates under integral curvature conditions, extending previous results to broader geometric settings.

Findings

Derived bounds for the first eigenvalue of the p-Laplacian

Extended eigenvalue estimates to manifolds with integral curvature bounds

Provided tools for further geometric analysis under integral curvature assumptions

Abstract

We give various estimates of the first eigenvalue of the $p$-Laplace operator on closed Riemannian manifold with integral curvature conditions.