Interior Curvature Bounds For Spacelike Hypersurfaces Of Prescribed <i>k</i>-th Mean Curvature

We derive interior curvature bounds for strictly spacelike hypersurfaces of prescribed k-th mean curvature in Minkowski space analogous to those we derived in previous work on the Euclidean case. The estimates depend on a sufficiently large L^p norm of the mean curvature. Examples similar to those in the Euclidean case show that if k ≥ 3, such curvature bounds are generally false if p is not sufficiently large.

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Published 1 January 2003