Rigidity of conformally compact manifolds with the round sphere as the conformal infinity
Rigidity of conformally compact manifolds with the round sphere as the conformal infinity
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DOI：
10.1016/j.aim.2009.12.004
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发表时间：
2008-01
影响因子：
1.7
通讯作者：
Satyaki Dutta
中科院分区：
文献类型：
--
作者：
Satyaki Dutta
本文证明了在Ricci曲率的下界和标量曲率渐近性的假设下，一个共形紧流形的共形边界为圆球的完全共形紧流形必须是双曲空间。它推广了类似的先前的结果，即在里奇曲率上施加更强的条件或对维度施加限制。
In this paper, we prove that under a lower bound on the Ricci curvature and an assumption on the asymptotic behavior of the scalar curvature, a complete conformally compact manifold whose conformal boundary is the round sphere has to be the hyperbolic space. It generalizes similar previous results where stronger conditions on the Ricci curvature or restrictions on dimension are imposed.