Abstract:The $L_p$-Minkowski problem deals with the existence of closed convex hypersurface with prescribed $p$-area measure. The problem has been solved in the sub-critical case $p>-n-1$, but remains widely open 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.
Tencent Meeting：https://meeting.tencent.com/dm/3XD6v0egi6U2
Meeting ID：144-398-116
