Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold $M^{2}\times\mathbb{R}$

Li Chen; Dan-Dan Hu; Jing Mao; Ni Xiang

Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold $M^{2}\times\mathbb{R}$

Differential Geometry 2018-05-22 v3

Authors: Li Chen , Dan-Dan Hu , Jing Mao , Ni Xiang

Abstract

In this paper, for the Lorentz manifold $M^{2}\times\mathbb{R}$ , with $M^{2}$ a $2$ -dimensional complete surface with nonnegative Gaussian curvature, we investigate its space-like graphs over compact strictly convex domains in $M^{2}$ , which are evolving by the non-parametric mean curvature flow with prescribed contact angle boundary condition, and show that solutions converge to ones moving only by translation.

Keywords

translating surfaces non-parametric mean curvature flow Lorentz manifold space-like graphs contact angle boundary condition

Cite

@article{arxiv.1804.10864,
  title  = {Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold $M^{2}\times\mathbb{R}$},
  author = {Li Chen and Dan-Dan Hu and Jing Mao and Ni Xiang},
  journal= {arXiv preprint arXiv:1804.10864},
  year   = {2018}
}

Comments

13 papges. Two typos have been corrected in Lemma 3.3 of version 2. Comments are welcome

Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold $M^{2}\times\mathbb{R}$

Abstract

Keywords

Cite

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