On the conformal method for the Einstein constraint equations
General Relativity and Quantum Cosmology
2020-07-29 v4 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1812.06320,
title = {On the conformal method for the Einstein constraint equations},
author = {Michael T. Anderson},
journal= {arXiv preprint arXiv:1812.06320},
year = {2020}
}
Comments
Final version, 31 pages, To appear in ATMP