Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature

2007/07/07 by Pierre Bayard, Bayard, Pierre, Philippe Delanoë +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #math.AP #math.DG #msc:34C11 #msc:35J65 #msc:53C40

paper · pdf · doi:10.48550/arxiv.0707.1092

13 pages

arxiv created 2007/07/07 · arxiv updated 2009/12/01

Abstract

Existence and uniqueness in \Bbb R^n,1 of entire spacelike hypersurfaces contained in the future of the origin O and asymptotic to the light-cone, with scalar curvature prescribed at their generic point M as a negative function of the unit vector \overrightarrowOm pointing in the direction of \overrightarrowOM, divided by the square of the norm of \overrightarrowOM (a dilation invariant problem). The solutions are seeked as graphs over the future unit-hyperboloid emanating from O (the hyperbolic space); radial upper and lower solutions are constructed which, relying on a previous result in the Cartesian setting, imply their existence.

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