The Scaled Polarity transform and related inequalities
Abstract
In this paper we deal with generalizations of the Mahler volume product for log-concave functions. We show that the polarity transform A can be rescaled so that the Mahler product it induces has upper and lower bounds of the same asymptotics. We discuss a similar result for the J transform. As an application, we extend the K\"onig-Milman duality of entropy result to the class of geometric log-concave functions.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.