A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
type: Item
instance of: scholarly article
title: A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
zbMATH Open document ID: 1026.58018
author: D. Cordero-Erausquin
author: Robert J. McCann
author: Michael Schmuckenschlaeger
published in: Inventiones Mathematicae
publication date: 2002-08-08T00:00:00Z
review text: The aim of this paper is to extend important functional inequalities from the Euclidean case to an \(n\)-dimensional complete, connected, Riemannian \(C^2\)-manifold. These inequalities are interpolation inequalities. The main result is a Riemannian Borell-Brascamp-Lieb inequality. It has as significant corollaries various Riemannian \(p\)-mean inequalities. For instance, for \(p=0\) one obtains a Riemannian version of the Prékopa-Leindler inequality. The method of proof relies on the study of optimal mass transport.
Mathematics Subject Classification ID: 58E35
Mathematics Subject Classification ID: 28C99
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 1777215
zbMATH Keywords: interpolation inequalities
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: curvature
zbMATH Keywords: goedesics
zbMATH Keywords: optimal mass transport
Wikidata QID: Q64384704
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
full work available at URL: s002220100160
OpenAlex ID: W2006308315
DOI: 10.1007/S002220100160
description: scientific article; zbMATH DE number 1777215