Change search
CiteExportLink to record
Permanent link

Direct link
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
A Large Class of Non-Constant Mean Curvature Solutions of the Einstein Constraint Equations on an Asymptotically Hyperbolic Manifold
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
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.

Place, publisher, year, edition, pages
2012. Vol. 310, no 3, 705-763 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-27202DOI: 10.1007/s00220-012-1420-4ISI: 000301492300006OAI: oai:DiVA.org:kth-27202DiVA: diva2:375756
Note

QC 20120411

Available from: 2010-12-09 Created: 2010-12-09 Last updated: 2017-12-11Bibliographically approved
In thesis
1. The Einstein constraint equations on asymptotically hyperbolic manifolds
Open this publication in new window or tab >>The Einstein constraint equations on asymptotically hyperbolic manifolds
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:nbn:se:kth:diva-26379 (URN)978-91-7415-783-3 (ISBN)
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
2. A study of asymptotically hyperbolic manifolds in mathematical relativity
Open this publication in new window or tab >>A study of asymptotically hyperbolic manifolds in mathematical relativity
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of ve papers where certain problems arising in mathematical relativity are studied in the context of asymptotically hyperbolic manifolds.

In Paper A we deal with constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds. Conditions on the scalar field and its potential are given which lead to existence and non-existence results.

In Paper B we construct non-constant mean curvature solutions of the constraint equations on asymptotically hyperbolic manifolds. Our approach consists in decreasing a certain exponent appearing in the equations, constructing solutions of these sub-critical equations and then letting the exponent tend to its true value. We prove that if a certain limit equation admits no non-trivial solution, then the set of solutions of the constraint equations is non empty and compact. W ealso give conditions ensuring that the limit equation admits no nontrivial solution. This is a joint work with Romain Gicquaud.

In this Paper C we obtain Penrose type inequalities for asymptotically hyperbolic graphs. In certain cases we prove that equality is attained only by the anti-de Sitter Schwarzschild metric. This is a joint work with Mattias Dahl and Romain Gicquaud.

In Paper D we construct a solution to the Jang equation on an asymptotically hyperbolic manifold with a certain asymptotic behaviour at infinity.

In Paper E we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that when the mass tends to zero the metric converges uniformly tot he hyperbolic metric. This is a joint work with Mattias Dahl and Romain Gicquaud.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. vii, 52 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 12:05
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-102874 (URN)
Public defence
2012-10-15, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20120928

Available from: 2012-09-28 Created: 2012-09-27 Last updated: 2012-09-28Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Sakovich, Anna
By organisation
Mathematics (Div.)
In the same journal
Communications in Mathematical Physics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 44 hits
CiteExportLink to record
Permanent link

Direct link
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