Ricci Curvature on Alexandrov spaces and Rigidity Theorems

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.

final version

References in corpus (1)

• Alexandrov meets Lott--Villani--Sturm

Cited by in corpus (4)

• Convergence of Non-Symmetric Diffusion Processes on RCD spaces
• A Simple Sampling Method for Metric Measure Spaces
• Ricci curvature, entropy and optimal transport
• On $\mathsf{CD}$ spaces with nonnegative curvature outside a compact set