On the infinitesimal versions of Log Brunn Minkowski and Gaussian Brunn Minkowski conjectures

Stochastics Seminar
Thursday, February 18, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 006
School of Mathematics, Georgia Tech
Log Brunn-Minkowski conjecture was proposed by Boroczky, Lutwak, Yang and Zhang in 2013. It states that in the case of symmetric convex sets the classical Brunn-MInkowski inequality may be improved. The Gaussian Brunn-MInkowski inequality was proposed by Gardner and Zvavitch in 2007. It states that for the standard Gaussian measure an inequality analogous to the additive form of Brunn_minkowski inequality holds true for symmetric convex sets. In this talk we shall discuss a derivation of an equivalent infinitesimal versions of these inequalities for rotation invariant measures and a few partial results related to both of them as well as to the classical Alexander-Fenchel inequality.