Nicholas Cheng-Hoong Chin, Frederick Tsz-Ho Fong, Jingbo Wan
Published 2018-12-06Version 1
It has been known in that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and many other 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 some other flows in the Euclidean space which evolves by diffeomorphisms generated by conformal Killing fields.
Inverse Mean Curvature Flow of Rotationally Symmetric Hypersurfaces
A class of inverse curvature flows for star-shaped hypersurfaces evolving in a cone
Regularity of inverse mean curvature flow in asymptotically hyperbolic manifolds with dimension $3$
![QR code for arXiv:1812.02396 [math.DG]](http://oss.arxitics.com/images/favicon.svg)