题目：A Variant of the Log Brunn-Minkowski Inequality
报告人：蒋美跃 教授 （北京大学）
摘要：Let K,L be symmetric convex bodies in R^n; h_K, h_L be the support functions of K,L, respectively, the following log Brunn-Minkowski inequality conjecture was proposed by Boroczky-Lutwak-Yang-Zhang (Adv. Math. 2012).
∫_(S^(n-1))〖log h_L/h_K 〗dV_K≥V(K)/n log V(L)/V(K) ,where V(L) and V(K) are the volumes of L and K, dV_K=1/n h_K dS_K with dS_K being the surface measure of K. They also showed that this is a stronger version of the classical Brunn-Minkowski inequality for symmetric convex bodies and the inequality (1) holds for n = 2.
In this talk after reviewing this inequality in 2-d we will propose and discuss a variant of this inequality for non-symmetric convex bodies and some related results.
All are welcome!