报告人：蒋美跃教授

北京大学

报告题目：ORLICZ-MINKOWSKI PROBLEM FOR POLYTOPES

报告时间：2017年04月26日14:30

报告地点：海韵数理楼661

报告摘要：The $L_p$-Minkowski problem in convex geometry can be stated as follows: given a real number $p$ and a Borel measure $\mu$ on $S^{n-1}$, not supported on a closed hemi-sphere,  find a convex body $K$ in $\mathbb R^n$ such that $0$ is in the interior of $K$ and the support function $h_K$ satisfies $$h_K^{1-p} d S_K =d\mu, $$ where $S_K$ is the surface measure of $K$.  In this talk we discuss a generalization. Given a function $\phi:(0,\infty)\to (0,\infty)$, find a convex body $K$ in $\mathbb R^n$ such that $$c \phi(h_K) d S_K =d\mu$$ for some constant $c>0$.Existence results for polytope case, that is, $\mu=\sum_1^N a_i \delta_{u_i}$ will be presented using the variational method. The results are based on a joint work with Wang Chu..

报告人简介：蔣美跃，北京大学数学研究所博士，北京大学数学学院教授、博士生导师。他在非线性泛函分析、临界点理论及其应用以及非线性偏微分方程和哈密顿系统等领域做了许多开创性工作。在A.I.H.P.-NA, Calc. Var., JDE等国际著名学术期刊发表学术论文多篇。

联系人：张文教授

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