报告题目:The Minkowski type problems for unbounded convex hypersurfaces
报告人:叶德平
报告时间:6月17日(星期一)16:15-17:15
报告地点:理学院1-301
英文摘要:
The classical Minkowski problem for convex bodies (i.e., compact convex sets) aims to find necessary and/or sufficient conditions on a pregiven measure \mu such that \mu is equal to the surface area measure of some convex body. Such a problem turns out to be central in many areas such as analysis, geometry, and PDEs. In this talk, I will talk about our recent progress on the Minkowski type problems for unbounded convex hypersurfaces. I will discuss their connections with Monge-Ampere type equations and present our solutions to these Minkowski type problems.
中文摘要:
紧致凸集上的经典Minkowski问题旨在找到使得给定测度\mu等于某个紧致凸集的曲面面积测度的充分或必要条件,在分析、几何和 PDE等许多领域都发挥着重要作用。本报告将介绍无界凸超曲面上Minkowski型问题的最新研究进展,以及它们与Monge-Ampere型方程的联系,最后给出Minkowski型问题的证明。
报告人简介:
叶德平,加拿大Memorial University终身教授。现任加拿大数学会旗舰杂志Canadian Journal of Mathematics和Canadian Mathematical Bulletin的副主编(Associate Editor),并于2017年获得JMAA Ames奖。长期从事凸几何分析、几何和泛函不等式、随机矩阵、量子信息理论和统计学等领域的研究,在 Comm. Pure Appl. Math.、Adv. Math.、J. Funct. Anal.、Math. Ann.、CVPDE等国际著名杂志发表论文40篇,主持加拿大国家自然科学基金(NSERC)项目。