Dorin Bucur

On Poincaré constants of convex bodies

In this talk I will review some classical sharp estimates for Poincaré constants of convex bodies in the Euclidean space in terms of their diameter, and I will present some improved inequalities which take into account the flatness of the domain. Special attention will be given to the geometric case of Poincaré constants related to optimal domain separation problems, for which a Bonnesen-type inequality can be derived, relying on some new result concerning bodies of constant width. Based on joint works with Vincenzo Amato and Ilaria Fragalà.