报告题目 (Title)：A Pólya–Szegő-type inequality for convex functions
中文标题：凸函数的 Pólya–Szegő-type不等式
报告人 (Speaker)：Fabian mussnig 萨尔茨堡大学
报告时间 (Time)：2025年11月21日（周五） 9:00-9:45
报告地点 (Place)：上海大学宝山校区FJ404
邀请人(Inviter)：席东盟、李晋、吴加勇
报告摘要：The classical Pólya–Szegő inequality can be seen as a far-reaching functional analog of the Euclidean isoperimetric inequality. Several generalizations are known, among which we want to highlight a version initially discovered by Klimov that considers simultaneous symmetrization of both the Sobolev function and the Young function.
We present a new Pólya–Szegő-type inequality for convex functions which coincides with Klimov's in special cases. Our approach builds upon a previous strategy of Klartag and connects mixed volumes of higher-dimensional convex bodies with mixed Monge–Ampère measures of convex functions.