Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold M²×ℝ

2018/04/29 by Li Chen, Chen, Li, Dan-Dan Hu +5
Mathematics · #35B45 #35K93 #53C42 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1804.10864

openalex publication_date 2018/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, for the Lorentz manifold M²×ℝ, with M² a 2-dimensional complete surface with nonnegative Gaussian curvature, we investigate its space-like graphs over compact strictly convex domains in M², 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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