(Download) "Spacelike Hypersurfaces with Constant Mean Curvature in the Steady State Space (Report)" by A. Gervasio de Lima, Henrique F. Colares # eBook PDF Kindle ePub Free
eBook details
- Title: Spacelike Hypersurfaces with Constant Mean Curvature in the Steady State Space (Report)
- Author : A. Gervasio de Lima, Henrique F. Colares
- Release Date : January 01, 2010
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 107 KB
Description
1 Introduction Interest in the study of spacelike hypersurfaces in Lorentzian manifolds has increased very much in recent years, from both the physical and mathematical points of view. For example, it was pointed out by J. Marsdan and F. Tipler in [16] and S. Stumbles in [22] that spacelike hypersurfaces with constant mean curvature in arbitrary spacetime play an important part in the relativity theory. They are convenient as initial hypersurfaces for the Cauchy problem in arbitrary spacetime and for studying the propagation of gravitational radiation. From a mathematical point of view, that interest is also motivated by the fact that these hypersurfaces exhibit nice Bernstein-type properties. Actually, E. Calabi in [6], for n [less than or equal to] 4, and S.Y. Cheng and S.T. Yau in [8], for arbitrary n, showed that the only complete immersed spacelike hypersurfaces of the (n + 1)-dimensional Lorentz-Minkowski space [L.sup.n+1] with zero mean curvature are the spacelike hyperplanes.
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