• DOI:10.1007/s00220-007-0203-9
• Corpus ID: 18940463

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}
}

• H. Bray, S. Hayward, +1 author W. Simon
• Published 7 March 2006
• Mathematics
• Communications in Mathematical Physics

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 uniformly expanding condition leaves a 1-parameter freedom, but for the whole family, the embedding functions satisfy a forward-backward parabolic system for which local existence does not hold in general. Nevertheless, we have obtained a generalization of the weak (distributional) formulation of this class of flows, generalizing the corresponding step of Huisken and Ilmanen’s proof of the Riemannian Penrose inequality.