Constant mean curvature spacelike hypersurfaces in standard static spaces: rigidity and parabolicity

DOI10.14492/HOKMJ/1602036027zbMath1457.53045OpenAlexW3092212985MaRDI QIDQ2212211

Henrique Fernandes de Lima, Adriano A. Medeiros, Eudes Leite de Lima, Eraldo A. jun. Lima

Publication date: 19 November 2020

Published in: Hokkaido Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.hokmj/1602036027

zbMATH Keywords

constant mean curvaturecomplete space-like hypersurfacesentire Killing graphsmaximal space-like surfacesstandard static spaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Cites Work

• Unnamed Item
• Constant mean curvature surfaces in warped product manifolds
• Parabolicity of maximal surfaces in Lorentzian product spaces
• Existence of maximal surfaces in asymptotically flat spacetimes
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• New examples of entire maximal graphs in \(\mathbb H^2 \times \mathbb R_1\)
• Complete spacelike hypersurfaces with constant mean curvature in \(-\mathbb R\times \mathbb H^n\)
• Calabi-Bernstein results for maximal surfaces in Lorentzian product spaces
• Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
• Complete CMC spacelike hypersurfaces immersed in a Lorentzian product space
• On the scalar curvature of hypersurfaces in spaces with a Killing field
• Harmonic functions on complete riemannian manifolds

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