Lower bounds for eigenvalues of Finsler manifolds

TL;DR

This paper establishes new lower bounds for eigenvalues of Finsler manifolds, improving existing estimates and analyzing the spectrum's multiplicities, with implications for geometric analysis.

Contribution

It introduces Gromov and Buser type lower bounds for eigenvalues on Finsler manifolds and enhances bounds for the Lusternik-Schnirelmann spectrum, including multiplicity estimates.

Findings

Derived Gromov and Buser type lower bounds for eigenvalues.

Improved lower bounds for the Lusternik-Schnirelmann spectrum.

Estimated multiplicities of eigenvalues.

Abstract

In this paper, we study the spectrums of faithful dimension pairs on a closed Finsler manifold and obtain a Gromov type and a Buser type lower bounds for eigenvalues. Furthermore, for the Lusternik-Schnirelmann spectrum, we not only obtain a better lower bound, but also estimate the multiplicity of each eigenvalue.