报告人：蒋美跃教授 北京大学
报告题目：$L_p$- Minkowski Problem for Polytopes
时 间：2016年4月22日 (星期五) 14:30
地 点：旗山校区数学研究中心学术报告厅
主 办：数学与计算机科学学院,福建省分析数学及应用重点实验室,数学研究中心
参加对象：感兴趣的老师和学生
报告摘要：The classical Minkowski Theorem states that: given aset of unit vectors $\{u_1,\cdots, u_m\}$ in $\mathbb R^n$ not lied on a closed hemisphere of $S^{n-1}$ and a set of positive numbers
$\{a_1,\cdots, a_m\}$, there is an m-faced polytope in $\mathbb R^n$ such that whose face have outer normals $u_1,\cdots, u_m$ and corresponding face-area $a_1,\cdots, a_m$ if and only if
$$
a_1 u_1+\cdots a_mu_m=0.
$$
The$L_p$Minkowski problem for polytopes concerns with the following problem: find necessary and sufficient conditions on a set of unit vectors $\{u_1,\cdots, u_m\}$ in $\mathbb R^n$ not lied on a closed hemisphere of $S^{n-1}$ and a set of positive numbers
$\{a_1,\cdots, a_m\}$such that there is an m-faced polytope in $\mathbb R^n$ containing the origin $0$ andwhose face have outer normals $u_1,\cdots, u_m$ and corresponding $L_p$ measure$a_1,\cdots, a_m$w.r.t. $0$.
In this talk we will report some results for this problem.
专家简介：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。
