On the optimal sets in Polya and Makai type inequalities

Abstract: 

In this talk we examine some shape functionals, introduced by Polya and Makai, involving the torsional rigidity and the first Dirichlet-Laplacian eigenvalue for bounded, open and convex sets of R^n. We establish new quantitative bounds, which give us key properties and information on the behavior of the optimizing sequences. In particular, we consider two kinds of reminder terms that provide information about the structure of these sequences, such as the thickness.

This is a joint work in collaboration with Vincenzo Amato and Nunzia Gavitone