Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
type: Item
instance of: scholarly article
title: Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
zbMATH Open document ID: 0855.58011
published in: Inventiones Mathematicae
publication date: 1997-02-20T00:00:00Z
full work available at URL: https://eudml.org/doc/144345
review text: The authors establish a Lévy-Gromov isoperimetric inequality for the invariant measure of an infinite-dimensional diffusion generator of positive curvature with isoperimetric model the Gaussian measure. This produces in particular a new proof of the Gaussian isoperimetric inequality. This isoperimetric inequality strengthens the classical logarithmic Sobolev inequality in this context. A local version for the heat kernel measures is also proved, which may then be extended into an isoperimetric inequality for the Wiener measure on the paths of a Riemannian manifold with bounded Ricci curvature (Theorem 5.1).
Mathematics Subject Classification ID: 58D20
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 856589
zbMATH Keywords: Lévy-Gromov isoperimetric inequality
zbMATH Keywords: invariant measure
zbMATH Keywords: infinite-dimensional diffusion generator
zbMATH Keywords: Gaussian measure
zbMATH Keywords: Gaussian isoperimetric inequality
zbMATH Keywords: Sobolev inequality
zbMATH Keywords: heat kernel measures
zbMATH Keywords: Wiener measure
author: Dominique Bakry
author: Michel Ledoux
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
OpenAlex ID: W1970185960
Wikidata QID: Q125100582
DOI: 10.1007/S002220050026
description: scientific article; zbMATH DE number 856589