Optimal transport and Ricci curvature in Finsler geometry
作者： Shin-ichi Ohta
关键词: Curvature of Riemannian manifolds 、 Mathematics 、 Mathematical analysis 、 Ricci decomposition 、 Riemann curvature tensor 、 Ricci flow 、 Pure mathematics 、 Sectional curvature 、 Ricci curvature 、 Scalar curvature 、 Finsler manifold
摘要: This is a survey article on recent progress (in [Oh3], [OS]) of the theory weighted Ricci curvature in Finsler geometry. Optimal transport plays an impressive role as developed Riemannian case by Lott, Sturm and Villani.
sci-hub.st 参考文章(32)
Cédric Villani, Optimal Transport: Old and New ,(2016)
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré, Gradient Flows: In Metric Spaces and in the Space of Probability Measures ,(2005)
David Bao, S-S Chern, Zhongmin Shen, None, An Introduction to Riemann-Finsler Geometry ,(2000)
Michel Ledoux, The concentration of measure phenomenon ,(2001)
Cédric Villani, Topics in Optimal Transportation ,(2003)
Zhongmin Shen, Lectures on Finsler Geometry ,(2001)
Jeff Cheeger, Tobias H. Colding, On the structure of spaces with Ricci curvature bounded below. I Journal of Differential Geometry. ,vol. 46, pp. 406- 480 ,(1997) , 10.4310/JDG/1214459974
John Lott, Cedric Villani, Ricci curvature for metric-measure spaces via optimal transport Annals of Mathematics. ,vol. 169, pp. 903- 991 ,(2009) , 10.4007/ANNALS.2009.169.903
Shin-ichi Ohta, Finsler interpolation inequalities Calculus of Variations and Partial Differential Equations. ,vol. 36, pp. 211- 249 ,(2009) , 10.1007/S00526-009-0227-4
Zhongmin Shen, Volume Comparison and Its Applications in Riemann–Finsler Geometry Advances in Mathematics. ,vol. 128, pp. 306- 328 ,(1997) , 10.1006/AIMA.1997.1630