We consider geometric flows of hypersurfaces expanding by a function of the extrinsic curvature and we show that the homothethic sphere is the unique solution of the flow which converges to a point at the initial time. The result does not require assumptions on the speed other than positivity and monotonicity and it is proved using a reflection argument. Our theorem shows that expanding flows exhibit stronger spherical rigidity, if compared with the classification results of ancient solutions in the contractive case.
Risa, S., Sinestrari, C. (2020). Strong spherical rigidity of ancient solutions of expansive curvature flows. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 52(2), 94-99 [10.1112/blms.12308].
Strong spherical rigidity of ancient solutions of expansive curvature flows
Risa S.;Sinestrari C.
2020-01-01
Abstract
We consider geometric flows of hypersurfaces expanding by a function of the extrinsic curvature and we show that the homothethic sphere is the unique solution of the flow which converges to a point at the initial time. The result does not require assumptions on the speed other than positivity and monotonicity and it is proved using a reflection argument. Our theorem shows that expanding flows exhibit stronger spherical rigidity, if compared with the classification results of ancient solutions in the contractive case.| File | Dimensione | Formato | |
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