Communications in Analysis and Geometry

Volume 11 (2003)

Number 2

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

Pages: 235 – 261

DOI: http://dx.doi.org/10.4310/CAG.2003.v11.n2.a4

Author

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 Lp 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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