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On the conformal method for the Einstein constraint equations
- Publication Year :
- 2018
-
Abstract
- In this work, we use the global analysis and degree-theoretic methods introduced by Smale to study the existence and multiplicity of solutions of the vacuum Einstein constraint equations given by the conformal method of Lichnerowicz-Choquet-Bruhat-York. In particular this approach gives a new proof of the existence result of Maxwell and Holst-Nagy-Tsogtgerel. We also relate the method to the limit equation of Dahl-Gicquaud-Humbert and the non-existence result of Nguyen.<br />Comment: Final version, 31 pages, To appear in ATMP
- Subjects :
- General Relativity and Quantum Cosmology
Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1812.06320
- Document Type :
- Working Paper