讲座编号：jz-yjsb-2022-y015

讲座题目：On the $Lp$-Minkowski problem with super-critical exponents

主 讲 人：李奇睿 教授 浙江大学

讲座时间：2022年5月5日（星期四）下午14:00

讲座地点：腾讯会议，会议ID:230 448 588

参加对象：数学与统计学院全体教师及研究生

主办单位：数学与统计学院、研究生院

主讲人简介：

浙江大学数学科学院研究员，博士生导师。研究方向是几何分析与完全非线性方程。近年来与合作者在最优运输问题，预定曲率问题，几何流等方向取得若干成果， 部分成果发表在 J. Eur. Math. Soc. (JEMS)、Adv. Math.、 Trans. Amer. Math. Soc. 、J. Funct. Anal.、Analysis&PDE、ARMA、CVPDE等期刊上。

主讲内容：

The $Lp$-Minkowski problem deals with the existence of closed convex hypersurface with prescribed $p$-area measure. It was known that the problem admits a solution in sub-critical case $p>-n-1$ and does not have a solution in general in the critical case $p=-n-1$. But it remains unknown in the super-critical case $p<-n-1$. In this talk, we introduce new ideas to solve the problem for all super-critical exponents. A crucial ingredient in the proof is a topological method based on the calculation of the homology of a topological space of ellipsoids. The talk is based on recent joint work with Qiang Guang and Xu-Jia Wang.