Einstein metrics with prescribed conformal infinity on the ball

@article{Graham1991EinsteinMW,
  title={Einstein metrics with prescribed conformal infinity on the ball},
  author={C. Robin Graham and John M. Lee},
  journal={Advances in Mathematics},
  year={1991},
  volume={87},
  pages={186-225}
}
In this paper we study a boundary problem for Einstein metrics. Let A4 be the interior of a compact (n + l)-dimensional manifold-with-boundary I@, and g a Riemannian metric on M. If 2 is a metric on bM, we say the conformal class [S] is the conformal infinity of g if, for some defining function p E P(ii;i) that is positive in A4 and vanishes to first order on bM, p2g extends continuously to A and p’g 1 TbM is conformal to g. It is clear that this an invariant notion, independent of the choice… Expand
On the structure of conformally compact Einstein metrics
Let M be an (n + 1)-dimensional manifold with non-empty boundary, satisfying π1(M, ∂M) = 0. The main result of this paper is that the space of conformally compact Einstein metrics on M is a smooth,Expand
A new proof of Lee’s theorem on the spectrum of conformally compact Einstein manifolds
Let M be a compact n + 1-dimensional manifold with boundary S. A Riemannian metric g on the interior M is conformally compact if for any defining function r of the boundary g = rg extends to a CExpand
Parabolic geometries as conformal infinities of Einstein metrics
The study of Einstein metrics is a central area of research in geometry and analysis, for both mathematical and physical reasons. The simplest examples of Einstein metrics are symmetric spaces. InExpand
Closedness of the Space of AHE Metrics on 4-Manifolds
Let M be a compact 4-manifold with boundary and consider the moduli space of asymptotically hyperbolic Einstein (AHE) metrics on M. Any such metric g induces a conformal class of metrics on theExpand
Einstein Metrics with Prescribed Conformal Infinity on 4-Manifolds
Abstract.This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribedExpand
Poincaré–Einstein metrics and the Schouten tensor
We examine the space of conformally compact metrics g on the interior of a compact manifold with boundary which have the property that the k th elementary symmetric function of the Schouten tensor AExpand
Unique continuation results for Ricci curvature
Unique continuation results are proved for metrics with prescribed Ricci curvature in the setting of bounded metrics on compact manifolds with boundary, and in the setting of complete conformallyExpand
2 1 M ay 2 00 1 Poincaré-Einstein metrics and the Schouten tensor
We examine here the space of conformally compact metrics g on the interior of a compact manifold with boundary which have the property that the kth elementary symmetric function of the SchoutenExpand
Existence of complete conformal metrics of negative Ricci curvature on manifolds with boundary
We show that on a compact Riemannian manifold with boundary there exists $${u \in C^{\infty}(M)}$$ such that, u|∂M ≡ 0 and u solves the σk-Ricci problem. In the case k = n the metric has negativeExpand
Math . Phys . 6 ( 2002 ) 307 – 327 dS / CFT and spacetime topology
In the general Euclidean formulation of the AdS/CFT correspondence put forth in [25], one considers Riemannian manifolds of the form M × Y , where M is conformally compactifiable with conformalExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 17 REFERENCES
ℋ -Space with a cosmological constant
  • C. LeBrun
  • Mathematics, Physics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1982
It is demonstrated that a real-analytic 3-manifold with Riemannian conformal metric is naturally the conformal infinity of a germ-unique real-analytic 4-manifold with real-analytic Riemannian metricExpand
Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
Abstract We give a detailed description of the Schwartz kernel of the resolvent of the Laplacian on a certain class of complete Riemannian manifolds with negative sectional curvature near infinity.Expand
Einstein metrics, spinning top motions and monopoles
On considere la construction de solutions pour l'equation d'Einstein autoduale. On applique la construction de Lebrun a la sphere de Berger: la 3-sphere de metrique σ 1 2 +σ 2 2 +I 3 σ 3 2 ou (σ 1 ,Expand
The Hodge cohomology of a conformally compact metric
On etudie le Laplacien de Hogde agissant sur des k-formes differentielles pour une classe de varietes de Riemann completes a courbure sectionnelle negative proche de l'infini. Ces varietes ont desExpand
Multiple Integrals in the Calculus of Variations
Semi-classical results.- The spaces Hmp and Hmp0.- Existence theorems.- Differentiability of weak solutions.- Regularity theorems for the solutions of general elliptic systems and boundary valueExpand
The Cauchy problem for Lorentz metrics with prescribed Ricci curvature
© Foundation Compositio Mathematica, 1983, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditionsExpand
Elliptic Partial Differential Equa-tions of Second Order
Chapter 1. Introduction Part I: Linear Equations Chapter 2. Laplace's Equation 2.1 The Mean Value Inequalities 2.2 Maximum and Minimum Principle 2.3 The Harnack Inequality 2.4 Green's RepresentationExpand
Transformation of boundary problems
II. PSEUDODIFFEI%ENTIAL OPERATORS i. Symbol spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 2. Operators on open sets . . . . . . . . . . . . . . . . . . . . . . . . . . 170 3.Expand
LEBRUN, X-space with a cosmological constant
  • Proc. Roy. Sot. London Ser. A
  • 1982
...
1
2
...