The mean curvature flow for isoparametric submanifolds
Differential Geometry
2019-12-02 v2
Abstract
A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite time to a smooth submanifold of lower dimension. We also give a precise description of the collapsing.
Keywords
Cite
@article{arxiv.0706.3550,
title = {The mean curvature flow for isoparametric submanifolds},
author = {Xiaobo Liu and Chuu-Lian Terng},
journal= {arXiv preprint arXiv:0706.3550},
year = {2019}
}
Comments
24 pages, PDF file