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arxiv: 1003.5948 · v3 · pith:XJ7CTMUHnew · submitted 2010-03-30 · 🧮 math.MG · math.DG· math.OC

Alexandrov meets Lott--Villani--Sturm

Anton Petrunin This is my paper
classification 🧮 math.MG math.DGmath.OC
keywords curvaturealexandrovboundlott--villani--sturmlowersenseboundscompatibility
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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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  1. Alexandrov spaces with non negative curvature and displacement convexity of the entropy tensor

    math.DG 2026-06 unverdicted novelty 7.0

    An Alexandrov space has nonnegative curvature if and only if its entropy tensor is matrix displacement convex, extending the smooth case via a constructed parallel trivialisation.