Abstract:

For a Finsler manifold with the weighted Ricci curvature bounded from below, we give Cheng type and Mckean type comparison theorems for the first eigenvalue of Finsler Laplacian. When the weighted Ricci curvature is nonnegative, we also obtain Calabi-Yau type volume growth theorem. These generalize and improve some recent literatures. Especially, by using the relationship of the counterparts between a Finsler metric and its reverse metric, we remove some restrictions on the reversibility.

Key words: Finsler manifold, Reversibility, The first eigenvalue, Comparison theorem, Volume growth