A stability result for translating spacelike graphs in Lorentz manifolds

In this paper, we investigate spacelike graphs defined over a domain Ω ⊂ M n in the Lorentz manifold M n × ℝ with the metric −d s 2 + σ , where M n is a complete Riemannian n -manifold with the metric σ, Ω has piecewise smooth boundary, and ℝ denotes the Euclidean 1-space. We prove an interesting stability result for translating spacelike graphs in M n × ℝ under a conformal transformation.