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arXiv · 2011.04200

Self-similar solutions to fully nonlinear curvature flows by high powers of curvature

Shanze Gao·Haizhong Li·Xianfeng Wang
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Abstract

In this paper, we investigate closed strictly convex hypersurfaces in $\mathbb{R}^{n+1}$ which shrink self-similarly under a large family of fully nonlinear curvature flows by high powers of curvature. When the speed function is given by powers of a homogeneous of degree $1$ and inverse concave function of the principal curvatures with power greater than $1$, we prove that the only such hypersurfaces are round spheres. We also prove that slices are the only closed strictly convex self-similar solutions to such curvature flows in the hemisphere $\mathbb{S}^{n+1}_{+}$ with power greater than or equal to $1$.

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Shanze Gao, Haizhong Li, Xianfeng Wang. 2020-11-09. Self-similar solutions to fully nonlinear curvature flows by high powers of curvature. https://arxiv.org/abs/2011.04200

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