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Uniqueness of maximal surfaces in generalized Robertson-Walker spacetimes and Calabi-Bernstein type problems. (English) Zbl 1185.53062

Summary: Complete maximal surfaces in generalized Robertson-Walker space-times obeying either the null convergence condition or the time-like convergence condition are studied. Uniqueness theorems that widely extend the classical Calabi-Bernstein theorem, as well as previous results on complete maximal surfaces in Robertson-Walker space-times, i.e. the case in which the Gauss curvature of the fiber is a constant, are given. All the entire solutions to the maximal surface differential equation in certain generalized Robertson-Walker space-times are found.

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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