Some remarks on the existence of spacelike hypersurfaces of constant mean curvature

1 November 1977

journal article
research article
Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society

Vol. 82 (3) , 489-495
https://doi.org/10.1017/s0305004100054153

Abstract

Bernstein's theorem states that the only complete minimal graphs in R3 are the hyperplanes. We shall produce evidence in favour of some conjectural generalizations of this theorem for the cases of spacelike hypersurfaces of constant mean curvature in Minkowski space and in de Sitter space. The results suggest that the class of asymptotically simple space-times admitting a complete spacelike hypersurface of constant mean curvature may well be considerably smaller than the general class of asymptotically simple space-times.

Keywords

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