Compactness of conformally compact Einstein manifolds in dimension 4

Sun Yung A. Chang; Yuxin Ge

doi:10.1016/j.aim.2018.10.010

Compactness of conformally compact Einstein manifolds in dimension 4

Sun Yung A. Chang, Yuxin Ge

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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 compactness of the boundary metrics at the conformal infinity, and on the topology of the manifolds.

Original language	English (US)
Pages (from-to)	588-652
Number of pages	65
Journal	Advances in Mathematics
Volume	340
DOIs	https://doi.org/10.1016/j.aim.2018.10.010
State	Published - Dec 15 2018

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Conformally compact Einstein manifolds
Fefferman–Graham compactification
Q-curvature
S-tensor

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10.1016/j.aim.2018.10.010

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title = "Compactness of conformally compact Einstein manifolds in dimension 4",

abstract = "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 compactness of the boundary metrics at the conformal infinity, and on the topology of the manifolds.",

keywords = "Conformally compact Einstein manifolds, Fefferman–Graham compactification, Q-curvature, S-tensor",

author = "Chang, {Sun Yung A.} and Yuxin Ge",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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AU - Ge, Yuxin

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N2 - 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 compactness of the boundary metrics at the conformal infinity, and on the topology of the manifolds.

AB - 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 compactness of the boundary metrics at the conformal infinity, and on the topology of the manifolds.

KW - Conformally compact Einstein manifolds

KW - Fefferman–Graham compactification

KW - Q-curvature

KW - S-tensor

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JF - Advances in Mathematics

ER -

Compactness of conformally compact Einstein manifolds in dimension 4

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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