Calculus of Variations and Geometric Measure Theory

A quantitative version of the Soap Bubble Theorem

Luigi Vezzoni

created by malchiodi on 29 Jan 2018
modified on 30 Jan 2018

2 feb 2018 -- 10:00   [open in google calendar]

Scuola Normale Superiore, Aula Mancini


The celebrated Soap Bubble Theorem of Alexandrov asserts that round spheres are the only closed constant mean curvature hypersurfaces embedded in the Euclidean space. The talk mainly focuses on the following quantitive version of the theorem.

The proof of the theorem, joint work with G.Ciraolo, makes use of a quantitive study of the method of the moving planes and the result implies a new pinching theorem for hypersurfaces in the Euclidean space. Furthermore, the theorem is optimal in a sense that it will be specified in the talk. The last part of the talk will be about an on-going study on the generalization of the result in space forms or, more generally, in warped product spaces.