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Article Dans Une Revue Journal of Geometric Analysis Année : 2011

Conformal compactification of asymptotically locally hyperbolic metrics

Résumé

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, 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.

Dates et versions

hal-00783636 , version 1 (01-02-2013)

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Eric Bahuaud, Romain Gicquaud. Conformal compactification of asymptotically locally hyperbolic metrics. Journal of Geometric Analysis, 2011, 21 (4), pp.1085-1118. ⟨10.1007/s12220-010-9179-3⟩. ⟨hal-00783636⟩
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