Bochner-Weitzenboeck formula and Li-Yau estimates on Finsler manifolds

内蕴与正规平均里奇曲率：简单 d-向量的 Bochner--Weitzenboeck 恒等式

Intrinsic and Normal Mean Ricci Curvatures: A Bochner--Weitzenboeck Identity for Simple d-Vectors

本文定义内蕴与正规平均里奇曲率，推导简单 d-向量的 Bochner--Weitzenboeck 恒等式，并应用于调和向量消失准则与 Hodge Laplacian 特征值下界。

Bochner-Weitzenböck formula and Li-Yau estimates on Finsler manifolds

We prove the Bochner-Weitzenböck formula for the (nonlinear) Laplacian on general Finsler manifolds and derive Li-Yau type gradient estimates as well as parabolic Harnack inequalities. Moreover, we deduce Bakry-Émery gradient estimates. All these estimates depend on lower bounds for the weighted flag Ricci tensor.

On Lower Bounds of the First Eigenvalue of Finsler-Laplacian

By using Bochner technique and gradient estimate, we give the lower bound estimates of the first eigenvalue of Finsler-Laplacian on Finsler manifolds. These results generalize the corresponding famous theorems in the Riemannian geometry.

Finsler几何的半群方法：Bakry-Ledoux等周不等式

A semigroup approach to Finsler geometry: Bakry-Ledoux's isoperimetric inequality

本文在Finsler流形上建立Bakry半群方法，由$L^1$-梯度估计与曲率下界推出Bakry-Ledoux高斯等周不等式，并推广至非可逆情形。

Some functional inequalities on non-reversible Finsler manifolds

We continue our study of geometric analysis on (possibly non-reversible) Finsler manifolds, based on the Bochner inequality established by the author and Sturm. Following the approach of the $Γ$-calculus a la Bakry et al, we show the dimensional versions of the Poincare--Lichnerowicz inequality, the logarithmic Sobolev inequality, and the Sobolev inequality. In the reversible case, these inequalities were obtained by Cavalletti--Mondino in the framework of curvature-dimension condition by means of the localization method. We show that the same (sharp) estimates hold also for non-reversible met…

Nonlinear geometric analysis on Finsler manifolds

This is a survey article on recent progress of comparison geometry and geometric analysis on Finsler manifolds of weighted Ricci curvature bounded below. Our purpose is two-fold: Give a concise and geometric review on the birth of weighted Ricci curvature and its applications; Explain recent results from a nonlinear analogue of the $Γ$-calculus based on the Bochner inequality. In the latter we discuss some gradient estimates, functional inequalities, and isoperimetric inequalities.