Gluing constructions for asymptotically hyperbolic manifolds with constant scalar curvature

Abstract

We show that asymptotically hyperbolic initial data satisfying smallness conditions in dimensions $n\ge 3$, or fast decay conditions in $n\ge 5$, or a genericity condition in $n\ge 9$, can be deformed, by a deformation which is supported arbitrarily far in the asymptotic region, to ones which are exactly Kottler ("Schwarzschild- adS") in the asymptotic region.

various minor changes and corrections

References in corpus (2)

• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds
• On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications