Regularity and rigidity of asymptotically hyperbolic manifolds
Regularity and rigidity of asymptotically hyperbolic manifolds
复制标题
渐近双曲流形的正则性和刚性
DOI：
10.1016/j.aim.2012.04.013
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Yuguang Shi
中科院分区：
文献类型：
--
作者：
Xue Hu;J. Qing;Yuguang Shi
本文研究了共形紧流形的一些本征性质。我们证明了，如果一个完备黎曼流形存在一个本质集，并且它的曲率在无穷远处以一定的速率趋近于- 1，那么它是共形紧化的，并且紧化的度量在无穷远处具有一定的规律性。结果证明了曲率以大于2的速率趋近于双曲的完全流形的一些刚性定理。
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 a consequence we prove some rigidity theorems for complete manifolds whose curvature tends to the hyperbolic one in a rate greater than 2.