标题：The Minkowski problem and Brunn-Minkowski type inequalities（凸几何系列课程）
主讲人：Karoly Boroczky（Alfréd Rényi Institute of Mathematics, Hungary）
邀请人：黄勇
时间：
2021年4月16日 16：00-19：00
2021年4月23日 16：00-19：00
2021年5月7日 16：00-19：00
2021年5月14日 16：00-19：00
地点：Zoom会议
摘要：The lecture series covers Brunn-Minkowski inequality, its functional version Prekopa Leindler inequality, the classical Minkowski problem, and some basic notions associated to convex bodies (support functions, mixed volumes, mean projections, surface area measures). On the one hand, the Lp and dual Minkowski problems are discussed. On the other hand, related geometric inequalities and conjectures are presented, like the Logarithmic Minkowski Conjecture. The talks are organized as follows:
We will first introduce the Brunn-Minkowski inequality for the linear combination of subsets of R^n and its functional version Prekopa-Leindler inequality, Brenier maps in optimal transportation, Minkowski content (surface area) of sets with Lipschitz boundary, and the Isoperimetric inequality.
2.Next, we will discuss convex bodies: Support function, Surface area measure, Mixed volumes, Minkowski inequality, Alexandrov Fenchel inequality, Mean projections, Centroid, John ellipsoid, Blaschke-Santalo inequality, Affine isoperimetric inequality, Steiner symmetrization.
3.Then, we will introduce Alexandrov's lemma, Minkowski problem, Regularity of the solution, Lp Minkowski problem, Lp Brunn-Minkowski inequality/conjecture, Cone volume measure, Logarithmic Minkowski problem, Logarithmic Minkowski Conjecture.
4.At last, we will discuss further variants of the Minkowski problem: Alexandrov problem, Christoffel-Minkowski problem, Lp Minkowski problem for p<0, Lp dual Minkowski problem, Gaussian and Orlicz versions.
