Generalized Inverse Mean Curvature Flows in Spacetime

@article{Bray2007GeneralizedIM,
  title={Generalized Inverse Mean Curvature Flows in Spacetime},
  author={Hubert L. Bray and Sean A. Hayward and Marc Mars and Walter Simon},
  journal={Communications in Mathematical Physics},
  year={2007},
  volume={272},
  pages={119-138}
}
Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking quasilocal mass is monotone. We focus on a subclass of such flows which we call uniformly expanding, which can be considered for null as well as for spacelike directions. In the null case, local existence of the flow is guaranteed. In the spacelike case, the… 
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