Spacelike Hypersurfaces with Constant Mean Curvature in the Steady State Space

作者：Gervasio Colarcs A; de Lima Hemrique F^*

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2010, 17(2): 287-302.

• Steady State space
• Spacelike hypersurface
• Mean curvature
• Height estimates
• Hyperbolic image

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 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 E(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 hyperplancs in H(n+1).

• 出版日期2010-6