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Communications in Mathematical Physics

, Volume 214, Issue 1, pp 137–189 | Cite as

Scalar Curvature Deformation and a Gluing Construction for the Einstein Constraint Equations

  • Justin Corvino

Abstract:

On a compact manifold, the scalar curvature map at generic metrics is a local surjection [F-M]. We show that this result may be localized to compact subdomains in an arbitrary Riemannian manifold. The method is extended to establish the existence of asymptotically flat, scalar-flat metrics on ℝ n (n≥ 3) which are spherically symmetric, hence Schwarzschild, at infinity, i.e. outside a compact set. Such metrics provide Cauchy data for the Einstein vacuum equations which evolve into nontrivial vacuum spacetimes which are identically Schwarzschild near spatial infinity.

Keywords

Manifold Riemannian Manifold Scalar Curvature Compact Manifold Curvature Deformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Justin Corvino
    • 1
  1. 1.Department of Mathematics, Stanford University, Stanford, CA 94305-2125, USA.¶E-mail: corvino@math.stanford.eduUS

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