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11
Renormalizing curvature integrals on PoincaréEinstein manifolds
, 2005
"... After analyzing renormalization schemes on a PoincaréEinstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is wellknown, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms ..."
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Cited by 27 (5 self)
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After analyzing renormalization schemes on a PoincaréEinstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is wellknown, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior under a variation of the PoincaréEinstein structure, and obtain, from the renormalized integral of the Pfaffian, an extension of the GaussBonnet theorem.
Dehn filling and Einstein metrics in higher dimensions
 J. Differential Geom
"... Abstract. We prove that many features of Thurston’s Dehn surgery theory for hyperbolic 3manifolds generalize to Einstein metrics in any dimension. In particular, this gives large, infinite families of new Einstein metrics on compact manifolds. 1. Introduction. In this paper, we construct a large ne ..."
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Cited by 25 (2 self)
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Abstract. We prove that many features of Thurston’s Dehn surgery theory for hyperbolic 3manifolds generalize to Einstein metrics in any dimension. In particular, this gives large, infinite families of new Einstein metrics on compact manifolds. 1. Introduction. In this paper, we construct a large new class of Einstein metrics of negative scalar curvature on ndimensional manifolds M = M n, for any n ≥ 4. Einstein metrics are Riemannian metrics g of constant Ricci curvature, and we will assume the curvature is normalized as (1.1) Ricg = −(n − 1)g,
TOPICS IN CONFORMALLY COMPACT EINSTEIN METRICS
, 2005
"... Conformal compactifications of Einstein metrics were introduced by Penrose [38], as a means to study the behavior of gravitational fields at infinity, i.e. the asymptotic behavior of solutions to the vacuum Einstein equations at null infinity. This has remained a very active area of research, cf. [2 ..."
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Cited by 13 (0 self)
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Conformal compactifications of Einstein metrics were introduced by Penrose [38], as a means to study the behavior of gravitational fields at infinity, i.e. the asymptotic behavior of solutions to the vacuum Einstein equations at null infinity. This has remained a very active area of research, cf. [27], [19] for recent surveys. In the context of Riemannian metrics, the
A CLASS OF COMPACT POINCARÉEINSTEIN MANIFOLDS: PROPERTIES AND CONSTRUCTION
, 2008
"... We develop a geometric and explicit construction principle that generates classes of PoincaréEinstein manifolds, and more generally almost Einstein manifolds. Almost Einstein manifolds satisfy a generalisation of the Einstein condition; they are Einstein on an open dense subspace and, in general, ..."
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Cited by 4 (3 self)
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We develop a geometric and explicit construction principle that generates classes of PoincaréEinstein manifolds, and more generally almost Einstein manifolds. Almost Einstein manifolds satisfy a generalisation of the Einstein condition; they are Einstein on an open dense subspace and, in general, have a conformal scale singularity set that is a conformal infinity for the Einstein metric. In particular, the construction may be applied to yield families of compact PoincaréEinstein manifolds, as well as classes of almost Einstein manifolds that are compact without boundary. We obtain classification results which show that the construction essentially exhausts a class of almost Einstein (and PoincaréEinstein) manifold. We develop the general theory of fixed conformal structures admitting multiple compatible almost Einstein structures. We also show that, in a class of cases, these are canonically related to a family of constant mean curvature totally umbillic embedded hypersurfaces.
ON THE STRUCTURE OF CONFORMALLY COMPACT EINSTEIN METRICS
"... Abstract. Let M be an (n+1)dimensional manifold with nonempty 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, infinite dimensional Banach manifold, provided it is nonempty. We also prove full boundary re ..."
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Cited by 3 (2 self)
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Abstract. Let M be an (n+1)dimensional manifold with nonempty 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, infinite dimensional Banach manifold, provided it is nonempty. We also prove full boundary regularity for such metrics in dimension 4 and a local existence and uniqueness theorem for such metrics with prescribed metric and stressenergy tensor at conformal infinity, again in dimension 4. This result also holds for LorentzianEinstein metrics with a positive cosmological constant. 1. Introduction. Let M be the interior of a compact (n + 1)dimensional manifold ¯ M with nonempty boundary ∂M. A complete metric g on M is C m,α conformally compact if there is a defining function ρ on ¯M such that the conformally equivalent metric (1.1) ˜g = ρ 2 g
WORMHOLES IN ACH EINSTEIN MANIFOLDS
, 2006
"... Abstract. We give a new construction of Einstein manifolds which are asymptotically complex hyperbolic, inspired by the work of MazzeoPacard in the real hyperbolic case. The idea is to develop a gluing theorem for 1handle surgery at infinity, which generalizes the Klein construction for the comple ..."
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Abstract. We give a new construction of Einstein manifolds which are asymptotically complex hyperbolic, inspired by the work of MazzeoPacard in the real hyperbolic case. The idea is to develop a gluing theorem for 1handle surgery at infinity, which generalizes the Klein construction for the complex hyperbolic metric. 1.
ASYMPTOTIC GLUING OF ASYMPTOTICALLY HYPERBOLIC SOLUTIONS TO THE EINSTEIN CONSTRAINT EQUATIONS
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