Gluing Constructions for Asymptotically Hyperbolic Manifolds with Constant Scalar Curvature
نویسنده
چکیده
We show that asymptotically hyperbolic initial data satisfying smallness conditions in dimensions n ≥ 3, or fast decay conditions in n ≥ 5, or a genericity condition in n ≥ 9, can be deformed, by a deformation which is supported arbitrarily far in the asymptotic region, to ones which are exactly Kottler (“SchwarzschildadS”) in the asymptotic region.
منابع مشابه
Connected Sum Constructions for Constant Scalar Curvature Metrics
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making “analytic” connected sums. In particular, we can easily construct complete metrics of constant positive scalar curvature on the complement of certain configurations of an even number of poin...
متن کاملGluing and wormholes for the Einstein constraint equations
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this handle region, the initial data sets we produce can be made as close as desired to the original initial data sets. These constructions can be made either...
متن کاملRecent advances in the global theory of constant mean curvature surfaces
The theory of complete surfaces of (nonzero) constant mean curvature in R has progressed markedly in the last decade. This paper surveys a number of these developments in the setting of Alexandrov embedded surfaces; the focus is on gluing constructions and moduli space theory, and the analytic techniques on which these results depend. The last section contains some new results about smoothing t...
متن کاملOn Stretch curvature of Finsler manifolds
In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied. In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...
متن کاملar X iv : d g - ga / 9 70 70 17 v 1 2 4 Ju l 1 99 7 SCALAR CURVATURE RIGIDITY FOR ASYMPTOTICALLY LOCALLY HYPERBOLIC MANIFOLDS
Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac operator defined with respect to the Killing connection. The existence of asymptotic Killing spinors is related to the spin structure on the end. The expressi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008