Constant mean curvature spacelike hypersurfaces in Lorentzian warped products and Calabi-Bernstein type problems

2014/01/28 by Juan A. Aledo, Alfonso Romero, Aledo, Juan A. +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #gr-qc #math.DG

paper · pdf · doi:10.48550/arxiv.1401.7687

arxiv created 2014/01/28 · openalex publication_date 2014/01/28 · arxiv updated 2014/01/31 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper we provide several uniqueness and non-existence results for complete parabolic constant mean curvature spacelike hypersurfaces in Lorentzian warped products under appropriate geometric assumptions. As a consequence of this parametric study, we obtain very general uniqueness and non-existence results for a large family of uniformly elliptic EDP's, so solving the Calabi-Bernstein problem in a wide family of spacetimes.

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