丘成桐中心几何与方程讨论班
SEU Yau Center Geometry and PDE Seminar
李海中 教授学术报告
Title: Hyperbolic p-sum and horospherical p-Brunn-Minkowski theory in hyperbolic space
Speaker: Prof. Haizhong Li（李海中）
Affiliation：Tsinghua University（清华大学）
Time: 15:00-16:00, May 10th (Wed.), 2023 (GMT+8)
Venue: 腾讯会议/VooV Meeting (ID: 645-898-102)
入会链接：https://meeting.tencent.com/dm/NkZHrjDCFGFc
Inviter: Yi Li（李逸），Jun Wang（王俊）
Abstract:
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 no Brunn-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.
Speaker:
李海中，清华大学二级教授，博士生导师。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.等数学期刊上发表论文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奖一等奖，2019年荣获国家自然科学奖二等奖。