Eigenvalue comparison theorems on Finsler manifolds

Abstract

Cheng-type inequality, Cheeger-type inequality and Faber-Krahn-type inequality are generalized to Finsler manifolds. For a compact Finsler manifold with the weighted Ricci curvature bounded from below by a negative constant, Li-Yau’s estimation of the first eigenvalue is also given.

Keywords

The first eigenvalue / Finsler-Laplacian / Ricci curvature / S-Curvature

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