On the shape of hypersurfaces with almost constant mean curvature

Title

On the shape of hypersurfaces with almost constant mean curvature

Speaker

Giulio Ciraolo - Palermo University

Abstract

Alexandrov’s theorem asserts that spheres are the only closed embedded hypersurfaces with constant mean curvature in the Euclidean space. In this talk we will discuss some quantitative versions of Alexandrov’s theorem. In particular, we will consider a hypersurface with mean curvature close to a constant and quantitatively describe its proximity to a sphere or to a collection of tangent spheres of equal radii in terms of the oscillation of the mean curvature. We will also discuss these issues for the nonlocal mean curvature, by showing a remarkable rigidity property of the nonlocal problem which prevents bubbling phenomena and proving the proximity to a single sphere

Bio

When

2019-04-02 at 3:00 pm (subject to variability)

Where

Genova