Ricci curvature and measures
type: Item
instance of: scholarly article
title: Ricci curvature and measures
zbMATH Open document ID: 1181.58026
author: Jean Pierre Bourguignon
published in: Japanese Journal of Mathematics. 3rd Series
publication date: 2009-12-09T00:00:00Z
review text: This article is based on the 5th Takagi Lectures delivered by Jean-Pierre Bourguignon at the University of Tokyo on October 4 and 5, 2008. It offers the general reader -- even those of us not steeped in Differential Geometry -- a fascinating glimpse and interesting account of the development, during the last thirty years, of the analysis of spaces whose Ricci curvature admits a lower bound. Starting from the classical context, it highlights the interaction between three different fields in mathematics, namely optimal transport theory, Riemannian geometry and probability theory. It is very helpful for students and young researchers in mathematics and physics who want to see a broader picture of the evolution of idea in this topic.
reviewed by: Raouf Ghomrasni
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 90B06
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 5644706
zbMATH Keywords: Ricci curvature
zbMATH Keywords: geometry of spaces of measures
zbMATH Keywords: Bakry-Émery estimate
zbMATH Keywords: optimal transport theory
zbMATH Keywords: lower bounds on curvature
zbMATH Keywords: Wasserstein distances
zbMATH Keywords: metric measured spaces
zbMATH Keywords: Gromov-Hausdorff topology
zbMATH Keywords: entropy functionals
MaRDI profile type: Publication
full work available at URL: s11537-009-0855-7
OpenAlex ID: W2009743695
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Wikidata QID: Q126199428
DOI: 10.1007/S11537-009-0855-7
description: scientific article; zbMATH DE number 5644706