Related papers: Topics in conformally compact Einstein metrics

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 prescribed conformal infinity, when the conformal infinity is…

The main result of this paper is that the space of conformally compact Einstein metrics on a given manifold is a smooth, infinite dimensional Banach manifold, provided it is non-empty, generalizing earlier work of Graham-Lee and Biquard. We…

In this paper, we establish some compactness results of conformally compact Einstein metrics on $4$-dimensional manifolds. Our results were proved under assumptions on the behavior of some local and non-local conformal invariants, on the…

This is a survey on the correspondence between asymptotically complex hyperbolic Einstein metrics and CR structures on the boundary at infinity, which is the complex version of that between Poincar\'e-Einstein metrics and conformal…

We survey some aspects of the current state of research on Einstein metrics on compact 4-manifolds. A number of open problems are presented and discussed.

We consider the problem of finding complete conformal metrics with prescribed curvature functions of the Einstein tensor and of more general modified Schouten tensors. To achieve this, we reveal an algebraic structure of a wide class of…

We study conformally compact metrics satisfying the Lovelock equations, which generalize the Einstein equation. We show that these metrics admit polyhomogeneous expansions, thereby naturally realizing the Fefferman-Graham expansion, which…

We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifolds in terms of certain Einstein and quasi-Einstein warped…

We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system…

This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.

Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.

This survey deals with two closely connected topics: first, the stability of Einstein metrics under the Einstein-Hilbert functional, and second, their deformation theory and the study of the moduli space of Einstein metrics on a compact…

This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the…

This article describes some geometric invariants and conformal anomalies for conformally compact Einstein manifolds and their minimal submanifolds which have recently been discovered via the Anti-de Sitter/Conformal Field Theory…

We show that C^2 conformally compact Riemannian Einstein metrics have conformal compactifications that are smooth up to the boundary in dimension 3 and all even dimensions, and polyhomogeneous in odd dimensions greater than 3.

A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…

In this paper, we establish compactness results of some class of conformally compact Einstein 4-manifolds. In the first part of the paper, we improve the earlier results obtained by Chang-Ge. In the second part of the paper, as…

We show that under some natural geometric assumption, Einstein metrics on conformal products of two compact conformal manifolds are warped product metrics.

In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological…

Given a metric defined on a manifold of dimension three, we study the problem of finding a conformal filling by a Poincar\'e-Einstein metric on a manifold of dimension four. We establish a compactness result for classes of conformally…