A Remark on a Uniqueness Property of High Multiplicity Tangent Flows in Dimension Three
Differential Geometry
2014-02-27 v1
Abstract
In this note, we combine the work of Ilmanen and of Colding-Ilmanen-Minicozzi to observe a uniqueness property for tangent flows at the first singular time of a smooth mean curvature flow of a closed surface in 3-dimensional Euclidean space. Specifically, if, at a fixed singular point, one tangent flow is a positive integer multiple of a shrinking plane, cylinder or sphere, then, modulo rotations, all tangent flows at the point are the same.
Keywords
Cite
@article{arxiv.1402.6687,
title = {A Remark on a Uniqueness Property of High Multiplicity Tangent Flows in Dimension Three},
author = {Jacob Bernstein and Lu Wang},
journal= {arXiv preprint arXiv:1402.6687},
year = {2014}
}
Comments
6 pages, 0 figure