报 告 人：盛为民教授

 浙江大学

报告题目：FLOW BY GAUSS CURVATURE TO THE ALEKSANDROV AND DUAL MINKOWSKI PROBLEMS

报告时间：2017年 3 月10 日上午 11:00

报告地点: 海韵实验楼108

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 $\alpha\ge n+1$, 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.

报告人简介：盛为民，浙江大学数学学院教授。、主要研究兴趣在于具有一定几何或物理背景的微分几何和偏微分方程，包括预定曲率问题，k-Yamabe问题，以及曲率流问题。其发表高水平数学论文30余篇在诸如Duke math. J., J. Diff. Geom., IMRN, CVPDE等一流杂志上。

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