Advances in Theoretical and Mathematical Physics

Volume 24 (2020)

Number 6

On the conformal method for the Einstein constraint equations

Pages: 1325 – 1374



Michael T. Anderson (Department of Mathematics, Stony Brook University, Stony Brook, New York, U.S.A.)


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 nonexistence result of Nguyen.

The author was partially supported by NSF grant DMS 1607479.

Published 7 July 2021