Ricci curvature on Alexandrov spaces and rigidity theorems

作者: Hui-Chun Zhang , Xi-Ping Zhu

DOI: 10.4310/CAG.2010.V18.N3.A4

关键词:

摘要: In this paper, we introduce a new notion for lower bounds of Ricci curvature on Alexandrov spaces, and extend Cheeger-Gromoll splitting theorem Cheng's maximal diameter to spaces under condition.

参考文章(22)
Shin-ichi Ohta, Optimal transport and Ricci curvature in Finsler geometry Probabilistic Approach to Geometry. pp. 323- 342 ,(2010) , 10.2969/ASPM/05710323
Cédric Villani, Optimal Transport: Old and New ,(2016)
Yukio Otsu, Takashi Shioya, The Riemannian structure of Alexandrov spaces Journal of Differential Geometry. ,vol. 39, pp. 629- 658 ,(1994) , 10.4310/JDG/1214455075
Kazuhiro Kuwae, Takashi Shioya, On Generalized Measure Contraction Property and Energy Functionals over Lipschitz Maps Potential Analysis. ,vol. 15, pp. 105- 121 ,(2001) , 10.1023/A:1011218425271
Dmitri Burago, Yuri Burago, Sergei Ivanov, A Course in Metric 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
Max-K. von Renesse, On local Poincaré via transportation Mathematische Zeitschrift. ,vol. 259, pp. 21- 31 ,(2008) , 10.1007/S00209-007-0206-4
Karl-Theodor Sturm, Convex functionals of probability measures and nonlinear diffusions on manifolds Journal de Mathématiques Pures et Appliquées. ,vol. 84, pp. 149- 168 ,(2005) , 10.1016/J.MATPUR.2004.11.002