Comparison Theorems and Their Applications on Kähler Finsler Manifolds

Abstract

We obtain complex Hessian and Laplacian comparison theorems on Kahler Finsler manifolds with holomorphic bisectional curvature bounded from below. As applications, we prove Bishop type volume comparison theorem and Myers type theorem for Kahler Finsler manifolds. Moreover, we also obtain some comparison theorems for the first eigenvalue of Finsler–Laplacian and give a sharp upper estimate of the bottom of the spectrum for Kahler Finsler manifolds whose holomorphic bisectional curvature is bounded from below by $$-\,1$$.