On Lower Bounds of the First Eigenvalue of Finsler-Laplacian

TL;DR

This paper establishes lower bounds for the first eigenvalue of the Finsler-Laplacian on Finsler manifolds using Bochner technique and gradient estimates, extending classical Riemannian results to Finsler geometry.

Contribution

It provides the first lower bound estimates for the Finsler-Laplacian eigenvalues, generalizing known Riemannian theorems to Finsler manifolds.

Findings

Lower bounds for the first eigenvalue derived

Generalization of Riemannian eigenvalue estimates

Application of Bochner technique to Finsler geometry

Abstract

By using Bochner technique and gradient estimate, we give the lower bound estimates of the first eigenvalue of Finsler-Laplacian on Finsler manifolds. These results generalize the corresponding famous theorems in the Riemannian geometry.