Georgia Institute of Technology College of Sciences

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.