Unique continuation results for Ricci curvature and applications
Unique continuation results for Ricci curvature and applications
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DOI：
10.1016/j.geomphys.2007.10.004
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发表时间：
2008-02-01
影响因子：
1.5
通讯作者：
Herzlich, Marc
中科院分区：
文献类型：
--
作者：
Anderson, Michael T.;Herzlich, Marc
证明了在有边界的紧致流形上的有界度量和完备共形紧度量下，具有指定Ricci曲率的度量的唯一延拓结果.与此相关，证明了一个等距扩张性质：在共形无穷远处的连续等距群扩张到任何完备共形紧爱因斯坦度量的体中。本文还讨论了这一性质与变形下Gauss-Codazzi约束方程的不变性之间的关系。(C)2007 Elsevier B. V.保留所有权利。
Unique continuation results are proved for metrics with prescribed Ricci curvature in the setting of bounded metrics on compact manifolds with boundary, and in the setting of complete conformally compact metrics on such manifolds. Related to this issue, an isometry extension property is proved: continuous groups of isometrics at conformal infinity extend into the bulk of any complete conformally compact Einstein metric. Relations of this property with the invariance of the Gauss-Codazzi constraint equations under deformations are also discussed. (C) 2007 Elsevier B.V. All rights reserved.