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arXiv · 2004.11754

Uniqueness of ancient solutions to Gauss curvature flow asymptotic to a cylinder

Beomjun Choi·Kyeongsu Choi·Panagiota Daskalopoulos
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Abstract

We address the classification of ancient solutions to the Gauss curvature flow under the assumption that the solutions are contained in a cylinder of bounded cross section. For each cylinder of convex bounded cross-section, we show that there are only two ancient solutions which are asymptotic to this cylinder: the non-compact translating soliton and the compact oval solution obtained by gluing two translating solitons approaching each other from time $-\infty$ from two opposite ends.

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Beomjun Choi, Kyeongsu Choi, Panagiota Daskalopoulos. 2020-04-24. Uniqueness of ancient solutions to Gauss curvature flow asymptotic to a cylinder. https://arxiv.org/abs/2004.11754

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