Homotopy of area decreasing maps by mean curvature flow

Andreas Savas-Halilaj; Knut Smoczyk

Homotopy of area decreasing maps by mean curvature flow

Differential Geometry 2013-02-05 v1 Analysis of PDEs

Authors: Andreas Savas-Halilaj , Knut Smoczyk

Abstract

Let $f:M\to N$ be a smooth area decreasing map between two Riemannian manifolds $(M,\gm)$ and $(N,\gn)$ . Under weak and natural assumptions on the curvatures of $(M,\gm)$ and $(N,\gn)$ , we prove that the mean curvature flow provides a smooth homotopy of $f$ to a constant map.

Keywords

mean curvature flow area decreasing maps Riemannian manifolds homotopy differential geometry

Cite

@article{arxiv.1302.0748,
  title  = {Homotopy of area decreasing maps by mean curvature flow},
  author = {Andreas Savas-Halilaj and Knut Smoczyk},
  journal= {arXiv preprint arXiv:1302.0748},
  year   = {2013}
}

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