报告人：陈敏（中国科学技术大学）

时间：2021年4月20日星期二9:00-11:00

腾讯会议：518 7997 8794

题目：The Minkowski problem in the sphere (Q. Guang, Q. R. Li, X. J. Wang)

摘要：Given a positive function $f$ on the unit sphere $\mathbb{S}_+^{n+1},$ the Minkowski problem in the sphere concerns the existence of convex hypersurfaces $M \subset \mathbb{S}_+^{n+1}$ such that the Gauss curvature of $M$ at $z$ is equal to $f(\nu(z))$, where $\nu(z)$ is the unit outer normal of $M$ at $z$. We use min-max principle the Gauss curvature flow to prove that there at least two solutions to the problem. By using the rotating plane method in the sphere, we also show the existence of a rotationally symmetric and monotone function $f$ such that there are exactly two solutions.