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arXiv · 1308.4095

Ancient solutions of the mean curvature flow

Robert Haslhofer·Or Hershkovits
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Abstract

In this short article, we prove the existence of ancient solutions of the mean curvature flow that for t -> 0 collapse to a round point, but for t -> -infinity become more and more oval: near the center they have asymptotic shrinkers modeled on round cylinders S^j x R^n-j and near the tips they have asymptotic translators modeled on Bowl^j+1 x R^n-j-1. We also give a characterization of the round shrinking sphere among ancient alpha-Andrews flows. Our proofs are based on the recent estimates of Haslhofer-Kleiner.

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Robert Haslhofer, Or Hershkovits. 2013-08-19. Ancient solutions of the mean curvature flow. https://arxiv.org/abs/1308.4095

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