Further inequalities for the Wills functional of convex bodies

Abstract: Michael Roysdon, Tel Aviv University, Israel

Topic:$L_p$-Brunn-Minkoswki type inequalities and an $L_p$-Borell-Brascamp-Lieb inequality, 10:30-10:50

Abstract: the classical Brunn-Minkowski inequality asserts that the volume of convex Minkowski combination exhibits (1/n)-concavity when applied for any pair of convex bodies (or more generally, Borel sets). Many advancements of this inequality have been studied throughout the year, famous examples of such mathematicians who pursued these studies are Prekopa, Leindler, and Brascamp and Lieb. The goal of this talk is to introduce the "L_p" versions of such inequalities following the L_p-Minkowski sum introduced by Firey (and later more generally by Lutwak, Yang, and Zhang), as well as it's associated L_p_ Brunn-Minkowksi inequality. In particular, we show that such inequalities hold in the class of s-concave measures, and discuss the related isoperimetric inequality (joint with S. Xing).

Jesús Yepes Nicolás, Universidad de Murcia, Spain

Topic: Further inequalities for the Wills functional of convex bodies.

Abstract: The Wills functional of a convex body, defined as the sum of its intrinsic volumes, turned out to have many interesting applications and properties. In this talk, making profit of the fact that it can be represented as the integral of a log-concave function, which is furthermore the Asplund product of other two log-concave functions, we will show new properties of the Wills functional. Among others, we get Brunn-Minkowski and Rogers-Shephard type inequalities for this functional and show that the cube of edge-length 2 maximizes it among all 0-symmetric convex bodies in John position. Joint work with David Alonso-Guti�rrez and Mar�a A. Hern�ndez Cifre.

analysis of PDEsmetric geometryprobability

Audience: researchers in the topic

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Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

If you are interested in giving a talk, please let one of the organizers know. Also, please suggest speakers which you would like to hear talk. Most talks are 50 minutes, but some 20-minute talks will be paired up as well. The talks will be video recorded conditioned upon the speakers' agreement.

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