AVVISO DI
SEMINARIO
ore
15.00
Scuola
Normale Superiore
Pisa
(Aula
Dini-Castelletto)
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."