The heat equation on manifolds as a gradient flow in the Wasserstein space
type: Item
instance of: scholarly article
title: The heat equation on manifolds as a gradient flow in the Wasserstein space
zbMATH Open document ID: 1215.35016
DOI: 10.1214/08-AIHP306
author: Matthias Erbar
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2010-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/241521
review text: The author considers the gradient flow of the relative entropy functional in the Wasserstein space \(P(M)\) of probability measures defined on the Riemannian manifold \(M\). In particular, a Riemannian structure on \(P(M)\) is introduced, by assuming the Ricci curvature of the manifold to be bounded below, the classical minimizing movements scheme is considered (existence) and the contractivity of the flow (uniqueness) is proved.
reviewed by: Ulisse Stefanelli
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 5717787
zbMATH Keywords: gradient flow
zbMATH Keywords: Wasserstein metric
zbMATH Keywords: relative entropy
zbMATH Keywords: heat equation
zbMATH Keywords: Riemannian manifold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5717787