Uniqueness Theorems of Self-Conformal Solutions to Inverse Curvature Flows
Differential Geometry
2020-04-29 v2
Abstract
It has been known in that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic curvature flows by degree -1 homogeneous functions of principle curvatures in the Euclidean space. In this article, we prove that the round sphere is rigid in much stronger sense, that under some natural conditions such as star-shapedness, it is the only closed solution to the inverse mean curavture flow and the above-mentioned flows in the Euclidean space which evolves by diffeomorphisms generated by conformal Killing fields.
Keywords
Cite
@article{arxiv.1812.02396,
title = {Uniqueness Theorems of Self-Conformal Solutions to Inverse Curvature Flows},
author = {Nicholas Cheng-Hoong Chin and Frederick Tsz-Ho Fong and Jingbo Wan},
journal= {arXiv preprint arXiv:1812.02396},
year = {2020}
}
Comments
15 pages; Theorems 3.1 and 4.5 rewritten; some remarks added. To appear in Proc. Amer. Math. Soc