Next Seminars

Paolo Valentini, University of L'Aquila, November 21, 2024 h 17:00-Aula Biancofiore, Coppito 1 

Alexandrov sphere theorems for W^{2,n}-hypersurfaces

Abstract: We extend classical results of Geometric Analysis such as Minkowski-Hsiung identities, Heintze-Karcher inequality and Alexandrov Soap Bubble theorems, to certain classes of domains in $\mathbb{R}^{n+1}$ whose topological boundary is representable locally as graphs of $W^{2,n}$-Sobolev functions. Our results are phrased in terms of the natural weak notion of curvature, associated with Sobolev graphs. A crucial point in the analysis is to construct a Legendrian cycle associated with these domains, exploiting Federer's theory of currents and fine properties of $W^{2,n}$-Sobolev functions.

Based on a joint work with Mario Santilli (University of L'Aquila).