講座編號(hào)：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(xué)
講座時(shí)間：2022年5月5日（星期四）下午14:00
講座地點(diǎn)：騰訊會(huì)議，會(huì)議ID:230 448 588
參加對(duì)象：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院全體教師及研究生
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、研究生院
主講人簡(jiǎn)介：
浙江大學(xué)數(shù)學(xué)科學(xué)院研究員，博士生導(dǎo)師。研究方向是幾何分析與完全非線性方程。近年來(lái)與合作者在最優(yōu)運(yùn)輸問(wèn)題，預(yù)定曲率問(wèn)題，幾何流等方向取得若干成果， 部分成果發(fā)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(nèi)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.