报告题目：Hyperbolic p-sum and horospherical p-Brunn-Minkowski theory in hyperbolic space

报告时间：2023年5月27日下午15:00-16:00.

报告地点：数学与统计学院310

报告人：清华大学博士生导师李海中教授

内容摘要： The classical Brunn-Minkowski theory studies the geometry of convex bodies in Euclidean space by use of the Minkowski sum. It originated from H. Brunn's thesis in 1887 and H. Minkowski's paper in 1903. Since there is no universally acknowledged definition of the sum of two sets in hyperbolic space, there has been noBrunn-Minkowski theory in hyperbolic space since 1903. In this talk, for any p>0 we introduce a sum of two sets in hyperbolic space, and we call it the hyperbolic p-sum. Then we develop a Brunn-Minkowski theory in hyperbolic space by use of our hyperbolic p-sum, and we call it the horospherical p-Brunn-Minkowski theory. This is joint work with Botong Xu.

报告人简介：李海中，清华大学二级教授，博士生导师，国务院政府特殊津贴获得者。从事微分几何的研究工作，在 JDG,Crelle’s Journal, Adv. Math.,Math. Ann., Trans. AMS, Calc. Var. PDE, JFA,Comm. Math. Phys., Math Z.等数学期刊发表论文160余篇，论文被国内外同行引用2000余次。与澳大利亚国立大学Ben Andrews教授合作给出三维球面中常平均曲率嵌入环面的完全分类，完全解决了著名的Pinkall-Sterling猜想。李海中教授2018年荣获教育部自然科学一等奖，2019年荣获国家自然科学二等奖。