Long-time existence of mean curvature flow with external force fields
Analysis of PDEs
2007-05-23 v1 Differential Geometry
Abstract
In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a long-time smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is convex with its eigenvalues satisfying a pinch inequality.
Cite
@article{arxiv.math/0611906,
title = {Long-time existence of mean curvature flow with external force fields},
author = {Yanan Liu and Huaiyu Jian},
journal= {arXiv preprint arXiv:math/0611906},
year = {2007}
}
Comments
17pages