5 papers
The Bonnet-Myers theorem on Finsler manifolds with integral weighted Ricci curvature bounds
Xinyue Cheng, Liulin Liu
In this paper, we derive some new relative volume comparison theorems and Bishop-Gromov volume comparisons on Finsler metric measure manifolds, all of which are controlled by the i…
Concentration and relevant properties of Finsler metric measure manifolds
Xinyue Cheng, Yalu Feng
In this paper, we study systematically the concentration properties of Finsler metric measure manifolds. We establish the relationships between the concentration properties and the…
Isoperimetric inequality on Finsler metric measure manifolds with non-negative weighted Ricci curvature
Xinyue Cheng, Yalu Feng, Liulin Liu
In this paper, we define the volume entropy and the second Cheeger constant and prove a sharp isoperimetric inequality involving the volume entropy on Finsler metric measure manifo…
On Finsler metric measure manifolds with integral weighted Ricci curvature bounds
Xinyue Cheng, Yalu Feng
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 Laplac…
Harnack inequality and the relevant theorems on Finsler metric measure manifolds
Xinyue Cheng, Yalu Feng
In this paper, we carry out in-depth research centering around the Harnack inequality for positive solutions to nonlinear heat equation on Finsler metric measure manifolds with wei…