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 twofold: give a concise and geometric review on the birth of weighted Ricci curvature and its applications; explain recent results...

Full description

Saved in:
Bibliographic Details
Published inEuropean journal of mathematics Vol. 3; no. 4; pp. 916 - 952
Main Author Ohta, Shin-ichi
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2017
Springer Nature B.V
Subjects
Algebraic Geometry
Calculus
Curvature
Inequalities
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Nonlinear analysis
Review Article
53C21
Heat flow
Isoperimetric inequality
53C60
58J35
Curvature
Finsler manifold
Functional inequality
Online AccessGet full text

Cover

More Information
Summary: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 Γ -calculus based on the Bochner inequality. In the latter we discuss some gradient estimates, functional inequalities, and isoperimetric inequalities.
ISSN:2199-675X
2199-6768
DOI:10.1007/s40879-017-0143-7