Mathematics

In this talk I will present some sharp spectral gap inequalities for the p-Laplace operator with Dirichlet boundary conditions on non smooth spaces with Ricci curvature bounded from below by K>0. These results, obtained in collaboration with Andrea Mondino, extend to this framework the classical ones by Bérard-Meyer and Matei. Attached to the aforementioned inequalities, in the setting of RCD(K,N) spaces we can obtain some rigidity and almost-rigidity results that seem to be new even in the cathegory of smooth Riemannian manifolds.