Regularity and rigidity of asymptotically hyperbolic manifolds

Details Regularity and rigidity of asymptotically hyperbolic manifolds Regularity and rigidity of asymptotically hyperbolic manifolds

2009-10-12

arxiv.org/abs/0910.2060v2

Mathematics

Differential Geometry

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Scientific paper

In this paper, we study some intrinsic characterization of conformally compact manifolds. We show that, if a complete Riemannian manifold admits an essential set and its curvature tends to -1 at infinity in certain rate, then it is conformally compactifiable and the compactified metrics can enjoy some regularity at infinity. As consequences we prove some rigidity theorems for complete manifolds whose curvature tends to the hyperbolic one in a rate greater than 2.

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