Hyperbolic inverse mean curvature flow
Abstract
In this paper, we prove the short-time existence of hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of () is mean convex and star-shaped. Several interesting examples and some hyperbolic evolution equations for geometric quantities of the evolving hypersurfaces have been shown. Besides, under different assumptions for the initial velocity, we can get the expansion and the convergence results of a hyperbolic inverse mean curvature flow in the plane , whose evolving curves move normally.
Cite
@article{arxiv.1710.01242,
title = {Hyperbolic inverse mean curvature flow},
author = {Zhe Zhou and Chuan-Xi Wu and Jing Mao},
journal= {arXiv preprint arXiv:1710.01242},
year = {2020}
}
Comments
35 pages. Hyperbolic inverse curvature flows in warped product manifolds have been discussed in [J. Mao, C.-X. Wu and Z. Zhou, Hyperbolic inverse curvature flows in warped products, preprint]. HIMCF of smooth strictly convex closed plane curves has been disscussed in v2 and some related interesting convergence and exanpansion results of the flow have also been shown. Comments are welcome