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.
Citation
Beomjun Choi. Kyeongsu Choi. Panagiota Daskalopoulos. "Uniqueness of ancient solutions to Gauss curvature flow asymptotic to a cylinder." J. Differential Geom. 127 (1) 77 - 104, May 2024. https://doi.org/10.4310/jdg/1717356155
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