[CvGmt News] Annuncio di Seminario
Luigi Ambrosio
luigi at ambrosio.sns.it
Wed Feb 9 09:57:59 CET 2005
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.
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