Intrinsic characterization for Lipschitz asymptotically hyperbolic metrics

Details Intrinsic characterization for Lipschitz asymptotically hyperbolic metrics Intrinsic characterization for Lipschitz asymptotically hyperbolic metrics

2007-11-21

arxiv.org/abs/0711.3371v2

Mathematics

Differential Geometry

18 pages; correction to Theorem 1

Scientific paper

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 asymptotically hyperbolic 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. We also present an interesting example that shows our conclusion is nearly optimal for our assumptions.

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