Translating Surfaces of the Non-parametric Mean Curvature Flow in Lorentz Manifold M ² × ℝ*

Abstract

In this paper, for the Lorentz manifold M ² × ℝ with M ² a 2-dimensional complete surface with nonnegative Gaussian curvature, the authors investigate its spacelike 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 / Mean curvature flow / Lorentz manifolds

References

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