Nonlinear geometric analysis on Finsler manifolds
Differential Geometry
2022-06-22 v2 Analysis of PDEs
Metric Geometry
Abstract
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 -calculus based on the Bochner inequality. In the latter we discuss some gradient estimates, functional inequalities, and isoperimetric inequalities.
Keywords
Cite
@article{arxiv.1704.01257,
title = {Nonlinear geometric analysis on Finsler manifolds},
author = {Shin-ichi Ohta},
journal= {arXiv preprint arXiv:1704.01257},
year = {2022}
}
Comments
37 pages (no change from v1); Corrigendum is available at http://www4.math.sci.osaka-u.ac.jp/~sohta/ ; See also my book "Comparison Finsler geometry" https://link.springer.com/book/10.1007/978-3-030-80650-7. arXiv admin note: text overlap with arXiv:1602.00390