Optimal transport and Ricci curvature in Finsler geometry

Shin‐ichi Ohta

doi:10.2969/aspm/05710323

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Optimal transport and Ricci curvature in Finsler geometry

Shin‐ichi Ohta

Year: 2019 Journal: Advanced studies in pure mathematics Pages: 323-342 Publisher: Mathematical Society of Japan

DOI: 10.2969/aspm/05710323

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Abstract

This is a survey article on recent progress (in [Oh3], [OS]) of the theory of weighted Ricci curvature in Finsler geometry. Optimal transport theory plays an impressive role as is developed in the Riemannian case by Lott, Sturm and Villani.

Keywords:

Ricci curvature Curvature Curvature of Riemannian manifolds Mathematics Geometry Ricci flow Finsler manifold Riemannian geometry Pure mathematics Scalar curvature Sectional curvature

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Advanced Differential Geometry Research

Physical Sciences → Physics and Astronomy → Astronomy and Astrophysics

Geometric Analysis and Curvature Flows

Physical Sciences → Mathematics → Applied Mathematics

Cosmology and Gravitation Theories

Physical Sciences → Physics and Astronomy → Astronomy and Astrophysics

Optimal transport and Ricci curvature in Finsler geometry

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