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arXiv · 2103.02314

Uniqueness of convex ancient solutions to hypersurface flows

Stephen Lynch
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Abstract

We show that every convex ancient solution of mean curvature flow with Type I curvature growth is either spherical, cylindrical, or planar. We then prove the corresponding statement for flows by a natural class of curvature functions which are convex or concave in the second fundamental form. Neither of these results assumes interior noncollapsing.

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Stephen Lynch. 2021-03-03. Uniqueness of convex ancient solutions to hypersurface flows. https://arxiv.org/abs/2103.02314

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