Compactness of conformally compact Einstein 4-manifolds II

2018/11/06 by Chang, Sun-Yung A., Yuxin Ge, Ge, Yuxin +2 · 2 citations
Mathematics · Physics and Astronomy · #53A30 #53C21 #53C25 #53C80 #58J05 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1811.02112

openalex publication_date 2018/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 applications, we derive some compactness results under perturbation conditions when the L²-norm of the Weyl curvature is small. We also derive the global uniqueness of conformally compact Einstein metrics on the 4-Ball constructed in the earlier work of Graham-Lee.

Citations

• Regularity of Einstein manifolds and the codimension 4 conjecture

Cited by

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

Related

• On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III
• Compactness of conformally compact Einstein manifolds in dimension 4
• On the topology of conformally compact Einstein 4-manifolds
• On the structure of conformally compact Einstein metrics
• Einstein metrics with prescribed conformal infinity on 4-manifolds