Perturbative solutions to the extended constant scalar curvature equations on asymptotically hyperbolic manifolds

Abstract

The extended constant scalar curvature equations is a particular case of the conformal contraint equations introduced by H. Friedrich. It was first studied by A. Butscher in an asymptotically flat setting. We prove the local existence of solutions to the extended constant scalar curvature equations near some asymptotically hyperbolic Einstein metrics. This gives a new local construction of asymptotically hyperbolic metrics with constant scalar curvature.