Nonlinear geometric analysis on Finsler manifolds
Nonlinear geometric analysis on Finsler manifolds
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DOI：
10.1007/s40879-017-0143-7
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发表时间：
2017-04
影响因子：
0.6
通讯作者：
Shin-ichi Ohta
中科院分区：
文献类型：
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作者：
Shin-ichi Ohta
本文综述了加权Ricci曲率下有界的Finsler流形的比较几何和几何分析的最新进展。我们的目的有两个：对加权Ricci曲率的产生及其应用进行了简明的几何回顾，解释了基于Bochner不等式的非线性微积分模拟的最新结果。在后者中，我们讨论了一些梯度估计，函数不等式和等周不等式。
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 twofold: 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-calculus based on the Bochner inequality. In the latter we discuss some gradient estimates, functional inequalities, and isoperimetric inequalities.