Geometry Colloquium

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.)

2014/06/26

10:00-11:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Kazumasa Kuwada (Tokyo Institute of Technology)
Entropic curvature-dimension condition and Bochner’s inequality (JAPANESE)
[ Abstract ]
As a characterization of "lower Ricci curvature bound and upper dimension bound”, there appear several conditions which make sense even on singular spaces. In this talk we show the equivalence in complete generality between two major conditions: a reduced version of curvature-dimension bounds of Sturm-Lott-Villani via entropy and optimal transport and Bakry–¥'Emery's one via Markov generator or the associated heat semigroup. More precisely, it holds for metric measure spaces where Cheeger's L^2-energy functional is a quadratic form. In particular, we establish the full Bochner inequality, which originally comes from the Bochner-Weitzenb¥"ock formula, on such spaces. This talk is based on a joint work with M. Erbar and K.-T. Sturm (Bonn).