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On maximal surfaces in certain non-flat 3-dimensional Robertson-Walker spacetimes. (English) Zbl 1255.53046

Summary: An upper bound for the integral, on a geodesic disc, of the squared length of the gradient of a distinguished function on any maximal surface in certain non-flat 3-dimensional Robertson-Walker space-times is obtained. As an application, a new proof of a known Calabi-Bernstein theorem is given.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
35J60 Nonlinear elliptic equations
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