On the higher order affine isoperimetric and affine Sobolev inequalities
数学专题报告
报告题目(Title)：On the higher order affine isoperimetric and affine Sobolev inequalities
报告人(Speaker)：Deping Ye （Memorial University of Newfoundland, Canada）
地点(Place)：后主楼1220
时间(Time)：2024年6月24日，15:30-16:30
邀请人(Inviter)：杨大春、袁文
报告摘要
The (affine) isoperimetric inequalities aim to find the maximum and/or minimum of (affine) functionals defined on convex bodies. Important examples include the classical isoperimetric inequality and the stronger affine isoperimetric inequality for Petty projection body. These inequalities have found their functional counterparts, namely the Sobolev and the affine Sobolev inequalities. They play fundamental roles in many areas, such as analysis, geometry, PDEs, etc.
In this talk, I will discuss the higher order affine isoperimetric and Sobolev inequalities. In particular, I will talk about the higher order Petty projection bodies and centroid bodies, present a variant of Steiner symmetrization being used to prove the higher order affine isoperimetric inequalities. I will also explain the functional setting, with concentration on the higher order affine Sobolev inequality for BV functions.
主讲人简介
Professor Deping Ye，2000年本科毕业于山东大学，2000-2003年于浙江大学读研， 2009年博士毕业于美国Case Western Reserve University，现为加拿大Memorial University终身教授，并主持加拿大国家自然科学基金(NSERC) 项目。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。 已在 Comm. Pure Appl. Math.，Adv. Math., J. Funct. Anal., Math. Ann., CVPDE等国际著名杂志（数学类， 数学物理类，和统计类） 上发表论文40篇。
