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arXiv · 1812.06320

On the conformal method for the Einstein constraint equations

Michael T. Anderson
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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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Michael T. Anderson. 2018-12-15. On the conformal method for the Einstein constraint equations. https://arxiv.org/abs/1812.06320

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