Alexandrov meets Lott--Villani--Sturm

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.