Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces - Couverture souple

Ambrosio, Luigi; Mondino, Andrea; Savare, Giuseppe

Couverture souple

ISBN 10 : 1470439131 ISBN 13 : 9781470439132

Editeur : American Mathematical Society, 2020

Synopsis

The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces $(X,\mathsf d,\mathfrak m)$.

On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of $K$-convexity when one investigates the convexity properties of $N$-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the $N$-dimensional entropy, in place of the heat flow.

Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong $\mathrm {CD}^{*}(K,N)$ condition of Bacher-Sturm.

A propos du livre

À propos de l'auteur

Luigi Ambrosio, Scuola Normale Superiore, Pisa, Italy.

Andrea Mondino, University of Warwick, Coventry, United Kingdom.

Giuseppe Savare, Universita di Pavia, Italy.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2020
• Langue: anglais
• ISBN 10: 1470439131
• ISBN 13: 9781470439132
• Reliure: Broché
• Nombre de pages: 121
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible