Mathematics

Estimates in geometric terms of the capacity  of compact sets are of great interest and appear naturally both in Geometry and Physics (e.g., in electrostatic and physical descriptions of flows where Laplace equation is used). I will discuss capacity inequalities involving the total mean curvature of hypersurfaces with boundary in convex cones and the mass of asymptotically flat manifolds with non-compact boundary. In fact, I will present analogs of Pölia-Szegö, Alexandrov-Fenchel and Penrose type inequalities in this setting.