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april 2010 Spacelike Hypersurfaces with Constant Mean Curvature in the Steady State Space
A. Gervasio Colares, Henrique F. de Lima
Bull. Belg. Math. Soc. Simon Stevin 17(2): 287-302 (april 2010). DOI: 10.36045/bbms/1274896207


In this paper we obtain height estimates concerning to a compact spacelike hypersurface $\Sigma^n$ immersed with constant mean curvature $H$ in the Steady State space $\mathcal H^{n+1}$, when its boundary is contained into some hyperplane of this spacetime. As a first application of these results, when $\Sigma^n$ has spherical boundary, we establish relations between its height and the radius of its boundary. Moreover, under a certain restriction on the Gauss map of $\Sigma^n$, we obtain a sharp estimate for $H$. Finally, we also apply our estimates to describe the end of a complete spacelike hypersurface and to get theorems of characterization concerning to spacelike hyperplanes in $\mathcal H^{n+1}$.


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A. Gervasio Colares. Henrique F. de Lima. "Spacelike Hypersurfaces with Constant Mean Curvature in the Steady State Space." Bull. Belg. Math. Soc. Simon Stevin 17 (2) 287 - 302, april 2010.


Published: april 2010
First available in Project Euclid: 26 May 2010

zbMATH: 1198.53059
MathSciNet: MR2663474
Digital Object Identifier: 10.36045/bbms/1274896207

Primary: 53C42
Secondary: 53B30 , 53C50

Keywords: Height estimates , Hyperbolic image , mean curvature , Spacelike hypersurface , Steady State space

Rights: Copyright © 2010 The Belgian Mathematical Society

Vol.17 • No. 2 • april 2010
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