AVVISO DI SEMINARIO

Giovedì 17 febbraio 2005 ore 15.00

Scuola Normale Superiore

Pisa

(Aula Dini-Castelletto)

Karl-Theodor Sturm Università di Bonn.

terrà un seminario dal titolo

"On the Geometry of Metric Measure Spaces"

Abstract

"We study the space of normalized metric measure spaces (M,d,m) and introduce a complete separable metric D on it. This metric has a natural interpretation in terms of mass transportation.

It turns out that the family of normalized metric measure spaces with doubling constant \le C is closed under D-convergence. Moreover, the subfamily of spaces with diameter \le R is compact.

Furthermore, we introduce and analyze curvature bounds for metric measure spaces (M,d,m), based on convexity properties of the relative entropy Ent(.|m). For Riemannian manifolds, Curv(M,d,m) \ge K if and only if Ric_M(v,v) \ge K |v|^2 for all v \in TM.

Our lower curvature bounds are stable under D-convergence."

Tutti gli interessati sono invitati ad intervenire.

- - - - - Scuola Normale Superiore Segreteria Classe di Scienze E-Mail: segreteria.scienze@sns.it - - - - -

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