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Complete vertical graphs with constant mean curvature in semi-Riemannian warped products. (English) Zbl 1160.53362
Summary: We study complete vertical graphs of constant mean curvature in the Hyperbolic and Steady State spaces. We first derive suitable formulas for the Laplacians of the height function and of a support-like function naturally attached to the graph; then, under appropriate restrictions on the values of the mean curvature and the growth of the height function, we obtain necessary conditions for the existence of such a graph. In the two-dimensional case we apply this analytical framework to state and prove Bernstein-type results in each of these ambient spaces.
MSC:
53C42Immersions (differential geometry)
53B30Lorentz metrics, indefinite metrics
53C50Lorentz manifolds, manifolds with indefinite metrics
53Z05Applications of differential geometry to physics
83C99General relativity