Uniqueness of mean curvature surfaces inmersed in a slab in certain Robertson-Walker spacetimes and Calabi Bernstein problems

Mathematics – Functional Analysis

Scientific paper

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Functional Analysis, Cosmology, Relativity, Differential Equations, Functional Analysis, Observational Cosmology, Initial Value Problem, Existence And Uniqueness Of Solutions, Ordinary And Partial Differential Equations, Boundary Value Problems

Scientific paper

Several uniqueness results for the spacelike slices in certain Robertson-Walker space-times are showed under boundedness assumptions either on the mean curvature function of the spacelike surface or on the restriction of the time coordinate on the surface when the mean curvature is constant. As an application of the results for the parametric case, we show a uniqueness result and non-existence one for bounded entire solutions of the some mean curvature constant spacelike differential equations.

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