Math @ Duke

Publications [#287084] of Hubert Bray
Papers Published
 Bray, H; Hayward, S; Mars, M; Simon, W, Generalized inverse mean curvature flows in spacetime,
Communications in Mathematical Physics, vol. 272 no. 1
(May, 2007),
pp. 119138, ISSN 00103616 [arXiv:grqc/0603014v1], [doi]
(last updated on 2017/12/11)
Abstract: 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 twosurfaces 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 1parameter freedom, but for the whole family, the embedding functions satisfy a forwardbackward 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. © SpringerVerlag 2007.


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