On generalizations of Grünbaum's inequality

Orateur: Francisco MARIN SOLA
Localisation: ,
Type: Séminaire informel analyse
Site: UGE , 4B 107
Date de début: 20/06/2023 - 10:30
Date de fin: 20/06/2023 - 11:30

A classical result by Grünbaum provides a sharp lower bound for the ratio $\text{vol}(K^-)/\text{vol}(K)$ of a convex body $K\subset \mathbb{R}^n$ that depends only on the dimension $n$ (here $K^-$ denotes the intersection of $K$ with a halfspace bounded by a hyperplane passing through its centroid).

In this work, on the one hand, we will discuss various recent results in the spirit of finding a generalization of Grünbaum's inequality, in both a geometric and a functional setting. On the other hand, we will show further generalizations of this result to the case of cuts (by hyperplanes) through other particular points.

This is part of joint work with David Alonso-Gutiérrez, Javier Martín-Goñi and Jesús Yepes Nicolás.