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arXiv · 2203.05259

Non-homothetic convex ancient solutions for flows by high powers of curvature

Susanna Risa·Carlo Sinestrari
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Abstract

We prove the existence of closed convex ancient solutions to curvature flows which become more and more oval for large negative times. The speed function is a general symmetric function of the principal curvatures, homogeneous of degree greater than one. This generalises previous work on the mean curvature flow and other one-homogeneous curvature flows. As an auxiliary result, we prove a new theorem on the convergence to a round point of convex rotationally symmetric hypersurfaces satisfying a suitable constraint on the curvatures.

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Susanna Risa, Carlo Sinestrari. 2022-03-10. Non-homothetic convex ancient solutions for flows by high powers of curvature. https://arxiv.org/abs/2203.05259

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