講座編號：jz-yjsb-2022-y015

講座題目：On the $Lp$-Minkowski problem with super-critical exponents

主 講 人：李奇睿 教授 浙江大學

講座時間：2022年5月5日（星期四）下午14:00

講座地點：騰訊會議，會議ID:230 448 588

參加對象：數學與統計學院全體教師及研究生

主辦單位：數學與統計學院、研究生院

主講人簡介：

浙江大學數學科學院研究員，博士生導師。研究方向是幾何分析與完全非線性方程。近年來與合作者在最優運輸問題，預定曲率問題，幾何流等方向取得若干成果， 部分成果發表在 J. Eur. Math. Soc. (JEMS)、Adv. Math.、 Trans. Amer. Math. Soc. 、J. Funct. Anal.、Analysis&PDE、ARMA、CVPDE等期刊上。

主講內容：

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.