Uniqueness of closed self-similar solutions to the Gauss curvature flow

Kyeongsu Choi; Panagiota Daskalopoulos

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arXiv · 1609.05487

Uniqueness of closed self-similar solutions to the Gauss curvature flow

Kyeongsu Choi·Panagiota Daskalopoulos

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Abstract

We show the uniqueness of strictly convex closed smooth self-similar solutions to the $\alpha$-Gauss curvature flow with $(1/n) < \alpha < 1+(1/n)$. We introduce a Pogorelov type computation, and then we apply the strong maximum principle. Our work combined with earlier works on the Gauss Curvature flow imply that the $\alpha$-Gauss curvature flow with $(1/n) < \alpha < 1+(1/n)$ shrinks a strictly convex closed smooth hypersurface to a round sphere.

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Kyeongsu Choi, Panagiota Daskalopoulos. 2016-09-18. Uniqueness of closed self-similar solutions to the Gauss curvature flow. https://arxiv.org/abs/1609.05487

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