中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：李奇睿 教授（浙江大学）
题 目： On the Lp-Minkowski problem with super-critical exponents
时 间：2022.07.20（星期三）下午14:00-15:00
地 点：腾讯会议：443-489-771
摘 要：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.