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The Einstein constraint equations on asymptotically hyperbolic manifolds
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2010 (English)Licentiate thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH , 2010. , 14 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 2010:14
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-26379ISBN: 978-91-7415-783-3 (print)OAI: oai:DiVA.org:kth-26379DiVA: diva2:372200
Presentation
2010-11-15, Sal D33, KTH, Lindstedtsvägen 5, Stockholm, 09:27
Opponent
Supervisors
Note
QC 20101209Available from: 2010-12-09 Created: 2010-11-24 Last updated: 2010-12-09Bibliographically approved
List of papers
1. Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds
Open this publication in new window or tab >>Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds
2010 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 27, no 24, 245019- p.Article in journal (Refereed) Published
Keyword
Einstein-scalar field equations, constraint equations, asymptotically hyperbolic manifold, conformal method, constant mean curvature
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-27201 (URN)10.1088/0264-9381/27/24/245019 (DOI)000284829400019 ()
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20101209 Uppdaterad från manuskript till published 20101221

Available from: 2010-12-09 Created: 2010-12-09 Last updated: 2017-12-11Bibliographically approved
2. A Large Class of Non-Constant Mean Curvature Solutions of the Einstein Constraint Equations on an Asymptotically Hyperbolic Manifold
Open this publication in new window or tab >>A Large Class of Non-Constant Mean Curvature Solutions of the Einstein Constraint Equations on an Asymptotically Hyperbolic Manifold
2012 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 310, no 3, 705-763 p.Article in journal (Refereed) Published
Abstract [en]

We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain exponent appearing in the equations, constructing solutions of these sub-critical equations and then in letting the exponent tend to its true value. We prove that the solutions of the sub-critical equations remain bounded which yields solutions of the constraint equation unless a certain limit equation admits a non-trivial solution. Finally, we give conditions which ensure that the limit equation admits no non-trivial solution.

National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-27202 (URN)10.1007/s00220-012-1420-4 (DOI)000301492300006 ()
Note

QC 20120411

Available from: 2010-12-09 Created: 2010-12-09 Last updated: 2017-12-11Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf