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.
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