In this paper,we study deeply geometric and topological properties of Finsler metric measure manifolds with the integral weighted Ricci curvature bounds.We first establish the Laplacian comparison theorem,the Bishop-G...In this paper,we study deeply geometric and topological properties of Finsler metric measure manifolds with the integral weighted Ricci curvature bounds.We first establish the Laplacian comparison theorem,the Bishop-Gromov-type volume comparison theorem and the relative volume comparison theorem on such Finsler manifolds.Then we obtain a volume growth estimate and Gromov pre-compactness for Finsler metric measure manifolds under the integral weighted Ricci curvature bounds.Furthermore,we prove the local Dirichlet isoperimetric constant estimate on Finsler metric measure manifolds with integral weighted Ricci curvature bounds.As applications of the Dirichlet isoperimetric constant estimates,we get the first Dirichlet eigenvalue estimate and a gradient estimate for harmonic functions.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12371051,12141101 and 11871126)。
文摘In this paper,we study deeply geometric and topological properties of Finsler metric measure manifolds with the integral weighted Ricci curvature bounds.We first establish the Laplacian comparison theorem,the Bishop-Gromov-type volume comparison theorem and the relative volume comparison theorem on such Finsler manifolds.Then we obtain a volume growth estimate and Gromov pre-compactness for Finsler metric measure manifolds under the integral weighted Ricci curvature bounds.Furthermore,we prove the local Dirichlet isoperimetric constant estimate on Finsler metric measure manifolds with integral weighted Ricci curvature bounds.As applications of the Dirichlet isoperimetric constant estimates,we get the first Dirichlet eigenvalue estimate and a gradient estimate for harmonic functions.
