A stability result for translating space-like graphs in Lorentz manifolds

Abstract

In this paper, we investigate space-like graphs defined over a domain $\Omega \subset M^n$ in the Lorentz manifold $M^n\times \mathbb{R}$ with the metric $-d{s}^2+\sigma$, where $M^n$ is a complete Riemannian $n$-manifold with the metric $\sigma$, $\Omega$ has piecewise smooth boundary, and $\mathbb{R}$ denotes the Euclidean $1$-space. We can prove an interesting stability result for translating space-like graphs in $M^n\times \mathbb{R}$ under a conformal transformation.

arXiv comment11 pages. Comments are welcome

References in corpus (2)

• The half-space property and entire positive minimal graphs in M x R
• Periodic constant mean curvature surfaces in H^2 x R

Cited by in corpus (3)

• Inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$
• An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$
• Curvature estimates for spacelike graphic hypersurfaces in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$