2011/09/23 by Romain Gicquaud, Gicquaud, Romain
Mathematics · Physics and Astronomy · #35J70 #53C21 #53C25 #58E10 #58J05 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · doi:10.48550/arxiv.1109.5096
openalex publication_date 2011/09/23 · openalex created_date 2023/03/21 · openalex updated_date 2026/07/28
In this paper we pursue the work initiated in \citeBahuaud, BahuaudGicquaud: study the extent to which conformally compact asymptotically hyperbolic metrics can be characterized intrinsically. We show how the decay rate of the sectional curvature to -1 controls the Hölder regularity of the compactified metric. To this end, we construct harmonic coordinates that satisfy some Neumann-type condition at infinity. Combined with a new integration argument, this permits us to recover to a large extent our previous result without any decay assumption on the covariant derivatives of the Riemann tensor. We believe that our result is optimal.