A sharp lower bound for the first eigenvalue on Finsler manifolds

TL;DR

This paper establishes a precise lower bound for the first nonzero Neumann eigenvalue of the Finsler-Laplacian on Finsler manifolds, linking it to geometric and curvature parameters.

Contribution

It provides the first sharp lower bound for the first eigenvalue of the Finsler-Laplacian based on diameter, dimension, and Ricci curvature.

Findings

Derived a sharp lower bound for the first eigenvalue

Connected eigenvalue estimates with geometric and curvature data

Enhanced understanding of spectral geometry on Finsler manifolds

Abstract

In this paper, we give a sharp lower bound for the first (nonzero) Neumann eigenvalue of Finsler-Laplacian in Finsler manifolds in terms of diameter, dimension, weighted Ricci curvature.