Mappings that preserve topological and/or algebraic structures such as e.g. 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.
Minkowski Endomorphisms
08.01.2025 11:30 - 13:00
Organiser:
T. Körber, A. Molchanova, F. Rupp
Location: