Alexandrov meets Lott--Villani--Sturm
Anton Petrunin

TL;DR
This paper demonstrates the compatibility of two different frameworks for defining generalized curvature bounds, linking Alexandrov's sectional curvature bounds with Lott--Villani--Sturm's Ricci curvature bounds.
Contribution
It establishes a connection between Alexandrov's and Lott--Villani--Sturm's curvature bounds, showing their compatibility in a unified framework.
Findings
Compatibility of Alexandrov and Lott--Villani--Sturm curvature bounds
Bridging sectional and Ricci curvature in generalized settings
Advancement in understanding curvature in metric measure spaces
Abstract
Here I show compatibility of two definition of generalized curvature bounds --- the lower bound for sectional curvature in the sense of Alexandrov and lower bound for Ricci curvature in the sense of Lott--Villani--Sturm.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Analytic and geometric function theory
