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Seminar

On the shape of hypersurfaces with almost constant mean curvature


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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


Bio


When

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


Where

Genova