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New proof of the Calabi-Bernstein theorem. (English) Zbl 1198.53061

Summary: By means of a local integral formula on a maximal surface, which involves the hyperbolic angle between the unit normal vector field and a fixed time-like direction, we give a new proof of the parametric Calabi-Bernstein theorem. A suitable modification of the integral formula gives an independent proof to the non-parametric case of this result.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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