Interior curvature bounds for spacelike hypersurfaces of prescribed k-th mean curvature

John Urbas

doi:10.4310/CAG.2003.v11.n2.a4

Interior curvature bounds for spacelike hypersurfaces of prescribed k-th mean curvature

John Urbas^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (SciVal)

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.

Original language	English
Pages (from-to)	235-261
Number of pages	27
Journal	Communications in Analysis and Geometry
Volume	11
Issue number	2
DOIs	https://doi.org/10.4310/CAG.2003.v11.n2.a4
Publication status	Published - Jun 2003

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10.4310/CAG.2003.v11.n2.a4

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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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AB - 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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Interior curvature bounds for spacelike hypersurfaces of prescribed k-th mean curvature

Abstract

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