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Mathematics > Differential Geometry

arXiv:0711.3371 (math)
[Submitted on 21 Nov 2007 (v1), last revised 11 Jul 2008 (this version, v2)]

Title:Intrinsic characterization for Lipschitz asymptotically hyperbolic metrics

Authors:Eric Bahuaud
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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 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.
Comments: 18 pages; correction to Theorem 1
Subjects: Differential Geometry (math.DG)
MSC classes: 53C21
Cite as: arXiv:0711.3371 [math.DG]
  (or arXiv:0711.3371v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0711.3371

Submission history

From: Eric Bahuaud [view email]
[v1] Wed, 21 Nov 2007 13:16:34 UTC (15 KB)
[v2] Fri, 11 Jul 2008 07:17:51 UTC (17 KB)
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