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Abstract
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Conformally compact
asymptotically hyperbolic metrics have been intensively studied. The goal
of this note is to understand what intrinsic conditions on a complete
Riemannian manifold (M,g) will ensure that g is AH in this sense. We use the
geodesic compactification by asymptotic geodesic rays to compactify M and
appropriate curvature decay conditions to study the regularity of the conformal
compactification.
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Keywords
asymptotically hyperbolic metric,
conformally compact metric, regularity of the geodesic
compactification
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Mathematical Subject Classification
Primary: 53C21
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Milestones
Received: 27 February 2008
Revised: 25 June 2008
Accepted: 15 September 2008
Published: 27 November 2008
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