Ricci Curvature on Alexandrov spaces and Rigidity Theorems

2009/12/16 by Hui-Chun Zhang, Zhang, Hui-Chun, Xi-Ping Zhu +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.0912.3190

openalex publication_date 2009/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• Finsler interpolation inequalities
• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products

Cited by

• Spaces with Riemannian curvature bounds are universally infinitesimally Hilbertian
• Generalized existence of extremizers for the sharp p-Sobolev inequality on Riemannian manifolds with nonnegative curvature

Related

• On a new definition of Ricci curvature on Alexandrov spaces
• Shape of Alexandrov spaces with positive Ricci curvature
• Rigidity for positively curved Alexandrov spaces with boundary
• Three-Dimensional Alexandrov spaces with positive or nonnegative Ricci curvature
• Alexandrov geometry: foundations