时间：2018年6月1日 星期五 10点

地点：3B106

报告人：浙江大学 盛为民 教授
题目：Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
摘要:  In this talk, I will introduce our recent work on Gauss curvature flow with Xu-Jia Wang and Qi-Rui Li. In this work we study a contracting flow of closed, convex hypersurfaces in the Euclidean space $\R^{n+1}$ with the speed $f r^{\alpha} K$, where $K$ is the Gauss curvature, $r$ is the distance from the hypersurface to the origin, and $f$ is a positive and smooth function. We prove that if $\alpha\gen+1$, the flow exists for all time and converges smoothly after normalization to a hypersurface, which is a sphere if $f\equiv 1$.  Our argument provides a new proof for the classical Aleksandrov problem  ($\alpha = n+1$) and resolves the dual q-Minkowski problem introduced by Huang, Lutwak, Yang and Zhang recently, for the case q<0 ($\alpha>n+1$). If $\alpha< n+1$, corresponding to the case q > 0, we also establish the same results for even function f and origin-symmetric initial condition, but for non-symmetric f, counterexample is given for the above smooth convergence.

盛为民教授简介：

盛为民，浙江大学教授、博士生导师，浙江大学数学学院副院长。1994年博士毕业于杭州大学，导师：白正国和沈一兵教授。研究方向是：微分几何与几何分析。在曲率流、高阶Yamabe问题和预定曲率问题方面做过重要工作，代表作发表于Duke Math J, JDG, Calc Var, Math Z.等高水平期刊上，另有文章在线发表于JEMS、Math.Ann.上。