Translating graphs by Mean curvature flow in $\M^n\times\Real$

Maria Calle; Leili Shahriyari

Translating graphs by Mean curvature flow in $\M^n\times\Real$

Differential Geometry 2014-06-05 v2

Authors: Maria Calle , Leili Shahriyari

Abstract

In this work, we study graphs in $\M^n\times\Real$ that are evolving by the mean curvature flow over a bounded domain on $\M^n$ , with prescribed contact angle in the boundary. We prove that solutions converge to translating surfaces in $\M^n\times\Real$ . Also, for a Riemannian manifold $\M^2$ with negative Gaussian curvature at each point, we show non-existence of complete vertically translating graphs in $\M^2\times\Real$ .

Keywords

mean curvature flow translating graphs prescribed contact angle negative Gaussian curvature non-existence Riemannian manifold

Cite

@article{arxiv.1109.5659,
  title  = {Translating graphs by Mean curvature flow in $\M^n\times\Real$},
  author = {Maria Calle and Leili Shahriyari},
  journal= {arXiv preprint arXiv:1109.5659},
  year   = {2014}
}

Comments

This paper has been withdrawn by the author due to a crucial error in one of references

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