Laplacian comparison on complex Finsler manifolds and its applications (Q2854044)

Many comparison theorems and their applications are known in real Finsler geometry, cf. [\textit{B.Y. Wu} and \textit{Y. L. Xin}, Math. Ann. 337, No. 1, 177--196 (2007; Zbl 1111.53060)]. In this paper, the authors prove the Rund Laplacian comparison theorem on complex Finsler manifolds with some applications. Using holomorphic variation of a geodesic curve on a complex Finsler space, they obtain the first and the second holomorphic variation formulas and an estimate for the Levi forms of distance function, corresponding to the complex Finsler metric. Also, two applications are emphasized: the Bonnet theorem and maximum principle on complex Finsler manifold.