Diff. Geom, Math. Phys., PDE: Fernando Schwartz

 I will begin this talk by recalling the classic inequalities of Alexandrov-Fenchel and Polya-Szego for convex surfaces of 3-dimensional Euclidean space.

Then, I will present my joint work with Freire, which generalizes the inequalities -with rigidity- to both a larger class of hypersurfaces and to arbitrary dimensions. I will conclude by mentioning some applications of the results, including a mass-capacity inequality for black holes.