Regularity and rigidity of asymptotically hyperbolic manifolds
Differential Geometry
2009-10-26 v2 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.0910.2060,
title = {Regularity and rigidity of asymptotically hyperbolic manifolds},
author = {Xue Hu and Jie Qing and Yuguang Shi},
journal= {arXiv preprint arXiv:0910.2060},
year = {2009}
}
Comments
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