Advanced Studies in Pure Mathematics

Optimal transport and Ricci curvature in Finsler geometry

Shin-ichi Ohta

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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.

Article information

Source
Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 323-342

Dates
Received: 7 January 2009
Revised: 5 March 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086327

Digital Object Identifier
doi:10.2969/aspm/05710323

Mathematical Reviews number (MathSciNet)
MR2648268

Zentralblatt MATH identifier
1205.53080

Subjects
Primary: 53C60: Finsler spaces and generalizations (areal metrics) [See also 58B20] 49Q20: Variational problems in a geometric measure-theoretic setting 58J35: Heat and other parabolic equation methods

Keywords
Finsler geometry optimal transport Ricci curvature comparison theorem

Citation

Ohta, Shin-ichi. Optimal transport and Ricci curvature in Finsler geometry. Probabilistic Approach to Geometry, 323--342, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710323. https://projecteuclid.org/euclid.aspm/1543086327


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