A Bernstein theorem for complete spacelike constant mean curvature hypersurfaces in Minkowski space |
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Authors: | Huai-Dong Cao Ying Shen Shunhui Zhu |
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Institution: | (1) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA (E-mail address: cao@math.tamu.edu) , US;(2) Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA (E-mail addresses: ying.shen@dartmouth.edu / shunhui.zhu@dartmouth.edu) , US |
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Abstract: | We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski
space into the hyperbolic space. As an application, 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 Pa] and Y.L. Xin Xin1] where they assume that the image of the Gauss map is
bounded. We also prove a Bernstein theorem for spacelike complete surfaces with parallel mean curvature vector in four-dimensional
spaces.
Received July 4, 1997 / Accepted October 9, 1997 |
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Keywords: | Mathematics Subject Classification (1991):Primary 53C21 53C42 |
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