Interior Curvature Bounds For Spacelike Hypersurfaces Of Prescribed k-th Mean Curvature

Research Report MRR01-022

Interior Curvature Bounds For Spacelike Hypersurfaces Of Prescribed k-th Mean Curvature

John Urbas

Abstract: 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\ge 3, such curvature bounds are generally false if p is not sufficiently large.

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