Compactness of conformally compact Einstein manifolds in dimension 4

2018/09/14 by Chang, Sun-Yung A., Yuxin Ge, Ge, Yuxin · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1809.05593

openalex publication_date 2018/09/14 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

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.

Cited by

• Poincaré-Einstein 4-manifolds with conformally Kähler geometry
• On the Poincaré-Einstein manifolds with cylindrical conformal infinity

Related

• Compactness of conformally compact Einstein 4-manifolds II
• Einstein metrics with prescribed conformal infinity on 4-manifolds
• On the problem of filling by a Poincaré-Einstein metric in dimension 4
• On the structure of conformally compact Einstein metrics
• On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III