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

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 $\M^2\times\Real$.

This paper has been withdrawn by the author due to a crucial error in one of references

References in corpus (1)

• Existence of a capillary surface with prescribed contact angle in $M\times \mathbb{R}$