A Bernstein theorem for complete spacelike constant mean curvature hypersurfaces in Minkowski space

Details A Bernstein theorem for complete spacelike constant mean curvature hypersurfaces in Minkowski space A Bernstein theorem for complete spacelike constant mean curvature hypersurfaces in Minkowski space

1997-09-07

arxiv.org/abs/dg-ga/9709011v1

Mathematics

Differential Geometry

22 pages, in LaTex

Scientific paper

We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As applications, we prove a Bernstein theorem which says that if the image of the Gauss map is bounded from one side, then the spacelike constant mean curvature hypersurface must be linear. This result extends the previous theorems obtained by B. Palmer and Y.L. Xin where they assume that the image of the Gauss map is bounded. We also proved a Bernstein theorem for spacelike complete surfaces with parallel mean curvature vector in four-dimensional spaces.

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