Inverse mean curvature flow inside a cone in warped products
Differential Geometry
2017-06-02 v3
Abstract
Given a convex cone in the \emph{prescribed} warped product, we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve along the inverse mean curvature flow, then, by using the convexity of the cone, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of round sphere as time tends to infinity.
Keywords
Cite
@article{arxiv.1705.04865,
title = {Inverse mean curvature flow inside a cone in warped products},
author = {Li Chen and Jing Mao and Ni Xiang and Chi Xu},
journal= {arXiv preprint arXiv:1705.04865},
year = {2017}
}
Comments
12 pages. Several minor revisions (including typos) have been made to v2