Comparison Theorems in Finsler Geometry with Integral Weighted Ricci Curvature Bounds and Their Applications

We establish the Laplacian comparison theorems and volume comparison theorems for Finsler manifolds under integral weighted Ricci curvature bounds. As their applications, we obtain some results on integral weighted Ricci curvature and topology for Finsler manifolds. We also obtain some results on the upper bound of first eigenvalue for Finsler manifolds under integral weighted Ricci curvature bounds.