学术报告：11月8号14:00-15:00，浙江大学--盛为民

报告人

盛为民

单位

浙江大学

报告题目

An Anisotropic shrinking flow and Lp   Minkowski problem

报告时间

2019.11.8

下午14:00-15:00

地点

第一报告厅

邀请人

潮小李

报告摘要

In this talk, I will introduce   my recent work with Caihong Yi on studying anisotropic shrinking flows and the   application on L_p Minkowski problem. We consider an shrinking flow of   smooth, closed, uniformly convex hypersurfaces in Euclidean R^{n+1} with   speed fu^\alpha\sigma_n^{-\beta}, where u is the support function of the   hypersurface, \alpha and \beta are two real numbers, and \beta>0, \sigma_n   is the n-th symmetric polynomial of the principle curvature radii of the   hypersurface. We prove that the flow exists an unique smooth solution for all   time and converges smoothly after normalisation to a smooth solution of the   equation fu^{\alpha-1}\sigma_n^{-\beta}=c provided the initial hypersuface is   origin-symmetric and f is a smooth positive even function on S^n for some   cases of \alpha and \beta. In the case \alpha>= 1+n\beta, \beta>0, we   prove that the flowconverges smoothly   after normalisation to a unique smooth solution of   fu^{\alpha-1}\sigma_n^{-\beta}=c without any constraint on the initial   hypersuface and the function f. When \beta=1, our argument provides a uniform   proof to the existence of the solutions to the L_p Minkowski problem   u^{1-p}\sigma_n=\phi for p\in(-n-1,+\infty) where \phi is a smooth positive   function on S^n.

报告人

简介

盛为民，浙江大学教授，博士生导师，数学科学学院副院长。主持国家自然科学基金面上项目4项，参与国家自然科学基金重点项目2项。研究兴趣是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，高阶Yamabe问题，以及曲率流问题。