Calculus of Variations and Geometric Measure Theory

Spherical rigidity of pinched ancient flows of hypersurfaces

Susanna Risa

created by root on 09 Apr 2019

11 apr 2019 -- 16:00   [open in google calendar]

sala seminari Dipartimento di Matematica Università di Pisa

Abstract.

A solution of a parabolic differential equation is ancient if it is defined for all negative times. They model the asymptotic shape of a compact submanifold evolving by a function of the extrinsic curvature as tangent flows if the second fundamental form blows up at a spherical scale. In 2014, Huisken and Sinestrari have shown that a uniform pinching condition on the curvature of a convex compact ancient solution of Mean Curvature Flow is sufficient to ensure it is a sphere shrinking by homotheties. An analogous result holds for more general fully nonlinear curvature flows: in particular, we consider spherical rigidity for evolutions by 1-homogeneous speeds and by powers of the Gaussian curvature.