Comparison theorems and their applications on Kähler Finsler manifolds
The current paper deals with comparision theorems and their applications on Kähler Finsler manifolds. The authors obtain complex Hessian and Laplacian comparision theorems on Kähler Finsler manifolds with holomorphic bisectional curvature bounded from below. As applications, they prove a Bishop-type volume comparision theorem and a Myers-type theorem for Kähler Finsler manifolds. Moreover, they also obtain some comparision theorems for the first eigenvalue of Finsler-Laplacian and give a sharp upper estimate of the bottom of the spectrum for Kähler Finsler manifolds whose holomorphic bisectional curvature is bounded from below by $-1$.
scientific article; zbMATH DE number 7187383
scientific article