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

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 3, such curvature bounds are generally false if p is not sufficiently large.