[CvGmt News] Annuncio di Seminario

[Luigi Ambrosio]

Vi giro un annuncio di seminario che non rientra tra quelli organizzati
da Giovanni Alberti. Siete tutti invitati a partecipare.

KARL-THEODOR STURM (University of Bonn)

``On the Geometry of Measure Metric Spaces''

Giovedi' 17.2 alle 15.00, nell'Aula Dini della SNS (in piazza del
Castelletto, di fronte all'ingresso della biblioteca di Scienze) 

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.