A note on spacelike hypersurfaces with prescribed mean curvature in a spatially closed globally static Lorentzian manifold. (English) Zbl 0658.53057
Let (M,g) be a Riemannian manifold and (\({\mathbb{R}}\times M, -\alpha^ 2dt^ 2\oplus g)\) a static Lorentzian warped product in which M is closed. The author proves that the Dirichlet problem for the mean curvature operator H has a (unique up to a constant) spacelike \(C^{2,\delta}\) solution if and only if \(\int_{M}H\alpha dv=0.\)
Reviewer: G.Pripoae
MSC:
53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |