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## Abstract In this paper, we investigate closed strictly convex hypersurfaces in R n + 1 {\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 S + n + 1 {\mathbb{S}^{n+1}\_{+}} with power greater than or equal to 1.

Author

Shanze Gao; Haizhong Li; Xianfeng Wang

Publisher

Walter de Gruyter GmbH

Published

2022

Language

EN