ML seminars - On the shape of hypersurfaces with almost constant mean curvature

Series

Analysis and Applications Seminar

Title

On the shape of hypersurfaces with almost constant mean curvature

Speaker

Giulio Ciraolo

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

Date

Tuesday, April 2nd, 2019

Time

3:00 p.m.

Location

DIMA - Room 705, via Dodecaneso 35, Genova