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Conformal Compactification of Asymptotically Locally Hyperbolic Metrics

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Abstract

In this paper we study the extent to which conformally compact asymptotically hyperbolic metrics may be characterized intrinsically. Building on the work of the first author in (Bahuaud, Pac. J. Math. 239(2): 231–249, 2009), we prove that decay of sectional curvature to −1 and decay of covariant derivatives of curvature outside an appropriate compact set yield Hölder regularity for a conformal compactification of the metric. In the Einstein case, we prove that the estimate on the sectional curvature implies the control of all covariant derivatives of the Weyl tensor, permitting us to strengthen our result.

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Authors and Affiliations

  1. Institut de Mathématiques et de Modélisation de Montpellier, UMR 5149 CNRS, Université Montpellier II, Case Courrier 051, Place Eugène Bataillon, 34095, Montpellier, France

    Eric Bahuaud & Romain Gicquaud

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  1. Eric Bahuaud
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  2. Romain Gicquaud
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Correspondence to Eric Bahuaud.

Additional information

Communicated by John M. Lee.

E. Bahuaud was partially supported by an ANR Postdoctoral grant, project GeomEinstein 06-BLAN-0154. R. Gicquaud partially supported by ANR project GeomEinstein 06-BLAN-0154.

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Bahuaud, E., Gicquaud, R. Conformal Compactification of Asymptotically Locally Hyperbolic Metrics. J Geom Anal 21, 1085–1118 (2011). https://doi.org/10.1007/s12220-010-9179-3

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  • DOI: https://doi.org/10.1007/s12220-010-9179-3

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