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arXiv · 1804.10864

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
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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.

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Li Chen, Dan-Dan Hu, Jing Mao, Ni Xiang. 2018-04-29. Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold $M^{2}\times\mathbb{R}$. https://arxiv.org/abs/1804.10864

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