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Publications [#303538] of Hubert Bray

Papers Published

  1. Bray, HL, A family of quasi-local mass functionals with monotone flows, edited by JC Zambrini (January, 2006), pp. 323-329, World Scientific, ISBN 981256201X [doi]
    (last updated on 2019/07/15)

    Abstract:
    © 2005 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. We define a one parameter family of quasi-local mass functionals mc(Σ), 0 ≤ c ≤ ∞, which are nondecreasing on surfaces in 3-manifolds with nonnegative scalar curvature with respect to a one parameter family of flows. In the case that c = 0, m0(Σ) equals the Hawking mass of Σ2and the corresponding flow is inverse mean curvature flow. Then, following the arguments of Geroch [8], Jang and Wald [12], and Huisken and Ilmanen [9], we note that the generalization of their results for inverse mean curvature flow would imply that if mADMis the total mass of the complete, asymptotically flat 3-manifold with nonnegative scalar curvature, then mADM≥ mc(Σ) for all nonnegative c and all connected surfaces Σ which are not enclosed by surfaces with less area.

 

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