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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}
}

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6 pages, 0 figure