报告题目 (Title)：Minkowski Endomorphisms
中文标题：Minkowski自同态
报告人 (Speaker)：Franz Schuster Vienna University of Technology
报告时间 (Time)：2025年11月19日（周三） 10:00-11:00
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：Mappings that preserve topological and/or algebraic structures such as isometries or homo-, iso-, and diffeomorphisms play a fundamental role in many areas of mathematics. In convex geometric analysis, an important class of such structure-preserving maps are the so-called Minkowski endomorphisms. In this talk we present classification results for Minkowski endomorphisms as well as a family of isoperimetric inequalities for monotone Minkowski endomorphisms, each one stronger than the classical Urysohn inequality. Among this large family of inequalities, the only affine invariant one – the Blaschke-Santaló inequality – turns out to be the strongest one. A further extension of these inequalities to merely weakly monotone Minkowski endomorphisms is proven to be impossible which, in turn, uncovers an unexpected phenomenon.