Math @ Duke

Publications [#303538] of Hubert Bray
Papers Published
 Bray, HL, A family of quasilocal mass functionals with monotone flows, edited by JC Zambrini
(January, 2006),
pp. 323329, 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 quasilocal mass functionals mc(Σ), 0 ≤ c ≤ ∞, which are nondecreasing on surfaces in 3manifolds 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 3manifold 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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