Conformal compactification of asymptotically locally hyperbolic metrics

Details Conformal compactification of asymptotically locally hyperbolic metrics Conformal compactification of asymptotically locally hyperbolic metrics

2008-11-25

arxiv.org/abs/0811.4184v1

J. Geom. Anal. 21 (2011), no. 4, 1085-1118

Mathematics

Differential Geometry

Scientific paper

10.1007/s12220-010-9179-3

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 H\"older 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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