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arXiv · 2205.00927

Closed self-similar solutions to flows by negative powers of curvature

Shanze Gao
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Abstract

In some warped product manifolds including space forms, we consider closed self-similar solutions to curvature flows whose speeds are negative powers of mean curvature, Gauss curvature and other curvature functions with suitable properties. We prove such self-similar solutions, not necessarily strictly convex for some cases, must be slices of warped product manifolds. A new auxiliary function is the key of the proofs.

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Shanze Gao. 2022-05-02. Closed self-similar solutions to flows by negative powers of curvature. https://arxiv.org/abs/2205.00927

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