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June 2020 Constant mean curvature spacelike hypersurfaces in standard static spaces: rigidity and parabolicity
Eudes L. de LIMA, Henrique F. de LIMA, Eraldo A. LIMA Jr., Adriano A. MEDEIROS
Hokkaido Math. J. 49(2): 297-323 (June 2020). DOI: 10.14492/hokmj/1602036027


Our purpose in this paper is investigate the geometry of complete constant mean curvature spacelike hypersurfaces immersed in a standard static space, that is, a Lorentzian manifold endowed with a globally defined timelike Killing vector field. In this setting, supposing that the ambient space is a warped product of the type $M^n\times_{\rho}\mathbb{R}_1$ whose Riemannian base $M^n$ has nonnegative sectional curvature and the warping function $\rho$ is convex on $M^n$, we use the generalized maximum principle of Omori-Yau in order to establish rigidity results concerning these spacelike hypersurfaces. We also study the parabolicity of maximal spacelike surfaces in $M^2\times_{\rho}\mathbb{R}_1$ and we obtain uniqueness results for entire Killing graphs constructed over $M^n$.


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Eudes L. de LIMA. Henrique F. de LIMA. Eraldo A. LIMA Jr.. Adriano A. MEDEIROS. "Constant mean curvature spacelike hypersurfaces in standard static spaces: rigidity and parabolicity." Hokkaido Math. J. 49 (2) 297 - 323, June 2020.


Published: June 2020
First available in Project Euclid: 7 October 2020

zbMATH: 07276077
MathSciNet: MR4159172
Digital Object Identifier: 10.14492/hokmj/1602036027

Primary: 53C42
Secondary: 53B30 , 53C50

Keywords: complete spacelike hypersurfaces , constant mean curvature , entire Killing graphs , maximal spacelike surfaces , Standard static spaces

Rights: Copyright © 2020 Hokkaido University, Department of Mathematics


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Vol.49 • No. 2 • June 2020
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