Conformal Compactification of Asymptotically Locally Hyperbolic Metrics
Conformal Compactification of Asymptotically Locally Hyperbolic Metrics
复制标题
渐近局部双曲度量的保角紧化
DOI：
10.1007/s12220-010-9179-3
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发表时间：
2008
影响因子：
1.1
通讯作者：
Romain Gicquaud
中科院分区：
文献类型：
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作者：
Eric Bahuaud;Romain Gicquaud
在本文中，我们研究共形紧渐近双曲度量的内在特征的程度。在第一作者的工作基础上（Bahuaud，Pac. J. Math. 239（2）：231-249，2009），我们证明了截面曲率衰减到−1和曲率的协变导数在适当的紧集之外的衰减产生度量的共形紧化的Hölder正则性。在爱因斯坦的情况下，我们证明，估计的截面曲率意味着控制的所有协变导数的外尔张量，使我们能够加强我们的结果。
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 in (Bahuaud, Pac. J. Math. 239(2): 231–249, 2009), we prove that decay of sectional curvature to −1 and decay of covariant derivatives of curvature outside an appropriate compact set yield Hölder 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.