Uniqueness theorems of self-conformal solutions to inverse curvature flows

Chin, Nicholas; Fong, Frederick; Wan, Jingbo

doi:10.1090/proc/15163

Uniqueness theorems of self-conformal solutions to inverse curvature flows
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by Nicholas Cheng-Hoong Chin, Frederick Tsz-Ho Fong and Jingbo Wan PDF

Proc. Amer. Math. Soc. 148 (2020), 4967-4982 Request permission

Abstract:

It is known from the literature 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 principal curvatures in the Euclidean space.

In this article, we prove that the round sphere is rigid in a stronger sense: under some natural conditions such as star-shapedness, round spheres are the only closed solutions to the above-mentioned flows which evolve by diffeomorphisms generated by conformal Killing fields.

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