Boundary Estimate of Asymptotically Hyperbolic Einstein Manifolds of Even Dimension

Abstract

In this paper, we study the finite boundary regularity and estimates of an asymptotically hyperbolic Einstein manifold in even dimension $n+1.$ We show that if the initial compactification is $C^{n-1}$ and the $(n-3)$-th derivative of its scalar curvature is Hölder continuous, then the AHE metric is $C^{m,\alpha }$ conformally compact provided the boundary metric is $C^{m,\alpha }$. This is an improvement of Helliwell's result. We also provide an estimate of the Yamabe compactification metric in the new structure.

18pages. arXiv admin note: text overlap with arXiv:1911.01885

References in corpus (2)

• The Ambient Obstruction Tensor and Q-Curvature
• On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III