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, ISBN 9789812704016 [doi]
(last updated on 2017/11/23)
Abstract: © 2005 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. We define a one parameter family of quasilocal mass functionals m c (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, m 0 (Σ) equals the Hawking mass of Σ 2 and 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 m ADM is the total mass of the complete, asymptotically flat 3manifold with nonnegative scalar curvature, then m ADM ≥ m c (Σ) for all nonnegative c and all connected surfaces Σ which are not enclosed by surfaces with less area.


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