報(bào)告題目：The Minkowski type problems for unbounded convex hypersurfaces

　　報(bào)告人：葉德平

　　報(bào)告時(shí)間：6月17日（星期一）16:15-17:15

　　報(bào)告地點(diǎn)：理學(xué)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：

　　緊致凸集上的經(jīng)典Minkowski問(wèn)題旨在找到使得給定測(cè)度\mu等于某個(gè)緊致凸集的曲面面積測(cè)度的充分或必要條件，在分析、幾何和 PDE等許多領(lǐng)域都發(fā)揮著重要作用。本報(bào)告將介紹無(wú)界凸超曲面上Minkowski型問(wèn)題的最新研究進(jìn)展，以及它們與Monge-Ampere型方程的聯(lián)系，最后給出Minkowski型問(wèn)題的證明。

　　報(bào)告人簡(jiǎn)介：

　　葉德平，加拿大Memorial University終身教授。現(xiàn)任加拿大數(shù)學(xué)會(huì)旗艦雜志Canadian Journal of Mathematics和Canadian Mathematical Bulletin的副主編(Associate Editor)，并于2017年獲得JMAA  Ames獎(jiǎng)。長(zhǎng)期從事凸幾何分析、幾何和泛函不等式、隨機(jī)矩陣、量子信息理論和統(tǒng)計(jì)學(xué)等領(lǐng)域的研究，在 Comm. Pure Appl. Math.、Adv. Math.、J. Funct. Anal.、Math. Ann.、CVPDE等國(guó)際著名雜志發(fā)表論文40篇，主持加拿大國(guó)家自然科學(xué)基金(NSERC)項(xiàng)目。