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arXiv · 0707.1092

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

Pierre Bayard·Philippe Delanoë
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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 $\overrightarrow{Om}$ pointing in the direction of $\overrightarrow{OM}$, divided by the square of the norm of $\overrightarrow{OM}$ (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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Pierre Bayard, Philippe Delanoë. 2007-07-07. Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature. https://arxiv.org/abs/0707.1092

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