Communications in Analysis and Geometry

Volume 17 (2009)

Number 2

Gluing constructions for asymptotically hyperbolic manifolds with constant scalar curvature

Pages: 343 – 381

DOI: http://dx.doi.org/10.4310/CAG.2009.v17.n2.a8

Authors

Piotr T. Chrusciel (Mathematical Institute and Hertford College, Oxford)

Erwann Delay (Laboratoire d’analyse non linéaire et géométrie, Faculté des Sciences, 33 rue Louis Pasteur, 84000 Avignon, France)

Abstract

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

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