Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 323 - 342
Optimal transport and Ricci curvature in Finsler geometry
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.
Received: 7 January 2009
Revised: 5 March 2009
First available in Project Euclid: 24 November 2018
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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