Low regularity Poincaré-Einstein metrics

2017/01/05 by Eric Bahuaud, John M. Lee, Bahuaud, Eric +1
Mathematics · Medicine · #53C25 #58J32 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Pelvic and Acetabular Injuries

paper · pdf · doi:10.48550/arxiv.1701.01481

openalex publication_date 2017/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of a C^1,1 conformally compact Einstein metric on the ball that has asymptotic sectional curvature decay to -1 plus terms of order e^-2r where r is the distance from any fixed compact set. This metric has no C² conformal compactification.

Related

• A Local Existence Result for Poincaré-Einstein metrics
• On the structure of conformally compact Einstein metrics
• Topics in conformally compact Einstein metrics
• Conformal metrics of the ball with constant σ_k-curvature and constant boundary mean curvature
• On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III