Methods and Applications of Analysis

Volume 16 (2009)

Number 1

Entire Scalar Curvature Flow and Hypersurfaces of Constant Scalar Curvature in Minkowski Space

Pages: 87 – 118

DOI: http://dx.doi.org/10.4310/MAA.2009.v16.n1.a6

Author

Pierre Bayard

Abstract

We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacelike hypersurface with constant scalar curvature. The proofs rely on barriers construction and a priori estimates.

Keywords

Entire graphs; prescribed scalar curvature; scalar curvature flow; Minkowski space

2010 Mathematics Subject Classification

35J60, 35K55, 53C50

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