On the conformal method for the Einstein constraint equations

Understand

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.