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arXiv · 1907.12319

Strong spherical rigidity of ancient solutions of expansive curvature flows

Susanna Risa·Carlo Sinestrari
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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.

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Susanna Risa, Carlo Sinestrari. 2019-07-29. Strong spherical rigidity of ancient solutions of expansive curvature flows. https://doi.org/10.1112/blms.12308

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