Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension

Brendan Guilfoyle; Wilhelm Klingenberg

doi:10.1090/tran/7766

Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension

Differential Geometry 2020-07-23 v2 Analysis of PDEs

Authors: Brendan Guilfoyle , Wilhelm Klingenberg

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Abstract

We prove long-time existence for mean curvature flow of a smooth $n$ -dimensional spacelike submanifold of an $n+m$ dimensional manifold whose metric satisfies the timelike curvature condition.

Keywords

mean curvature flow spacelike submanifold timelike curvature condition long-time existence higher codimension

Cite

@article{arxiv.1812.00710,
  title  = {Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension},
  author = {Brendan Guilfoyle and Wilhelm Klingenberg},
  journal= {arXiv preprint arXiv:1812.00710},
  year   = {2020}
}

Comments

19 pages LaTEX. Essentially this is Section 3 of the Proof of the Caratheodory Conjecture by the same authors, which is posted at arXiv:0808.0851

Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension

Abstract

Keywords

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