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Asymptotically hyperbolic extensions and an analogue of the Bartnik mass
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2018 (English)In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 132, p. 338-357Article in journal (Refereed) Published
Abstract [en]

The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these model time-symmetric domains obeying the dominant energy condition without a cosmological constant. There is a natural analogue of the Bartnik mass for asymptotically hyperbolic Riemannian manifolds with a negative lower bound on scalar curvature which model time-symmetric domains obeying the dominant energy condition in the presence of a negative cosmological constant. Following the ideas of Mantoulidis and Schoen (2016), of Miao and Xie (2018), and of joint work of Miao and the authors (Cabrera Pacheco et al., 2017), we construct asymptotically hyperbolic extensions of minimal and constant mean curvature (CMC) Bartnik data while controlling the total mass of the extensions. We establish that for minimal surfaces satisfying a stability condition, the Bartnik mass is bounded above by the conjectured lower bound coming from the asymptotically hyperbolic Riemannian Penrose inequality. We also obtain estimates for such a hyperbolic Bartnik mass of CMC surfaces with positive Gaussian curvature. 

Place, publisher, year, edition, pages
Elsevier B.V. , 2018. Vol. 132, p. 338-357
Keywords [en]
Asymptotically hyperbolic manifolds, Bounded scalar curvature, Quasi-local mass
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-236653DOI: 10.1016/j.geomphys.2018.06.010ISI: 000442066100022Scopus ID: 2-s2.0-85049837601OAI: oai:DiVA.org:kth-236653DiVA, id: diva2:1262823
Funder
Knut and Alice Wallenberg Foundation
Note

Correspondence Address: McCormick, S.; Institutionen för Matematik, Kungliga Tekniska Högskolan, Sweden; email: stephen.mccormick@math.uu.se; Funding details: Carl-Zeiss-Stiftung; Funding details: DMS 1452477, NSF, National Science Foundation; Funding details: ZUK 63, DFG, Deutsche Forschungsgemeinschaft; Funding details: Knut och Alice Wallenbergs Stiftelse; Funding details: Eberhard Karls Universität Tübingen; Funding text: All three authors thank the Erwin Schrödinger Institute for hospitality and support during theirvisits in 2017 in the context of the program Geometry and Relativity . AJCP and CC thank the Carl Zeiss foundation for generous support. The work of CC and SM was partially supported by the DAAD and Universities Australia . The work of AJCP was partially supported by the NSF grant DMS 1452477 . The work of CC is supported by the Institutional Strategy of the University of Tübingen (Deutsche Forschungsgemeinschaft, ZUK 63 ). SM is grateful for support from the Knut and Alice Wallenberg Foundation . QC 20181113

Available from: 2018-11-13 Created: 2018-11-13 Last updated: 2018-12-10Bibliographically approved

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