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McCormick, S. (2018). On a minkowski-like inequality for asymptotically flat static manifolds. Proceedings of the American Mathematical Society, 146(9), 4039-4046
Open this publication in new window or tab >>On a minkowski-like inequality for asymptotically flat static manifolds
2018 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, no 9, p. 4039-4046Article in journal (Refereed) Published
Abstract [en]

The Minkowski inequality is a classical inequality in differential geometry giving a bound from below on the total mean curvature of a convex surface in Euclidean space, in terms of its area. Recently there has been interest in proving versions of this inequality for manifolds other than ℝn; for example, such an inequality holds for surfaces in spatial Schwarzschild and AdS-Schwarzschild manifolds. In this note, we adapt a recent analysis of Y. Wei to prove a Minkowski-like inequality for general static asymptotically flat manifolds.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2018
National Category
urn:nbn:se:kth:diva-238339 (URN)10.1090/proc/14047 (DOI)000438582900037 ()2-s2.0-85049929419 (Scopus ID)

QC 20191115

Available from: 2018-11-15 Created: 2018-11-15 Last updated: 2019-01-22Bibliographically approved
Cabrera Pacheco, A. J., Cederbaum, C., McCormick, S. & Miao, P. (2017). Asymptotically flat extensions of CMC Bartnik data. Classical and quantum gravity, 34(10), Article ID 105001.
Open this publication in new window or tab >>Asymptotically flat extensions of CMC Bartnik data
2017 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 34, no 10, article id 105001Article in journal (Refereed) Published
Abstract [en]

Let g be a metric on the 2-sphere with positive Gaussian curvature and H be a positive constant. Under suitable conditions on (g, H), we construct smooth, asymptotically flat 3-manifolds M with non-negative scalar curvature, with outer-minimizing boundary isometric to and having mean curvature H, such that near infinity M is isometric to a spatial Schwarzschild manifold whose mass m can be made arbitrarily close to a constant multiple of the Hawking mass of . Moreover, this constant multiplicative factor depends only on (g, H) and tends to 1 as H tends to 0. The result provides a new upper bound of the Bartnik mass associated with such boundary data.

Place, publisher, year, edition, pages
Institute of Physics Publishing, 2017
Bartnik mass, constant mean curvature surfaces, Hawking mass, scalar curvature
National Category
Physical Sciences
urn:nbn:se:kth:diva-216533 (URN)10.1088/1361-6382/aa6921 (DOI)000413778300001 ()2-s2.0-85018988148 (Scopus ID)

Funding details: DAAD, Deutscher Akademischer Austauschdienst; Funding text: The work of CC and SM was partially supported by the DAAD and Universities Australia. CC is indebted to the Baden-Wrttemberg Stiftung for the financial support of this research project by the Eliteprogramme for Postdocs.

QC 20171124

Available from: 2017-11-24 Created: 2017-11-24 Last updated: 2017-11-24Bibliographically approved

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