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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.

53C42Immersions (differential geometry)
53B30Lorentz metrics, indefinite metrics
53C50Lorentz manifolds, manifolds with indefinite metrics
53Z05Applications of differential geometry to physics
83C99General relativity
Full Text: Euclid