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 Cn-1 and the (n-3)-th derivative of its scalar curvature is H\"older continuous, then the AHE metric is Cm,α conformally compact provided the boundary metric is Cm,α. This is an improvement of Helliwell's result. We also provide an estimate of the Yamabe compactification metric in the new structure.
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