PRESCRIBING GAUSS CURVATURE OF SURFACES IN 3-DIMENSIONAL SPACETIMES APPLICATION TO THE MINKOWSKI PROBLEM

@inproceedings{Bguin2008PRESCRIBINGGC,
  title={PRESCRIBING GAUSS CURVATURE OF SURFACES IN 3-DIMENSIONAL SPACETIMES APPLICATION TO THE MINKOWSKI PROBLEM},
  author={François B{\'e}guin and ABDELGHANI ZEGHIB},
  year={2008}
}
— We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with constant non-negative curvature is foliated by compact spacelike surfaces with constant Gauss curvature. In the constant negative curvature case, such a foliation exists outside the convex core. The existence of these foliations, together with a theorem of C… CONTINUE READING

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