Intrinsic characterization for Lipschitz asymptotically hyperbolic metrics

Eric Bahuaud

Vol. 239 (2009), No. 2, 231–249

DOI: 10.2140/pjm.2009.239.231

Abstract

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.

Keywords

asymptotically hyperbolic metric, conformally compact metric, regularity of the geodesic compactification

Mathematical Subject Classification 2000

Primary: 53C21

Milestones

Received: 27 February 2008

Revised: 25 June 2008

Accepted: 15 September 2008

Published: 27 November 2008