11东南大学数学学院邀请专家申请表
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。 | ||
