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Mathematics > Differential Geometry

arXiv:0710.1305 (math)
[Submitted on 5 Oct 2007 (v1), last revised 10 Mar 2008 (this version, v2)]

Title:Unique continuation results for Ricci curvature and applications

Authors:Michael T. Anderson, Marc Herzlich
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Abstract: 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. Related to this issue, an isometry extension property is proved: continuous groups of isometries 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.
Comments: 32 pages, supercedes math.DG/0501067; final published version
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:0710.1305 [math.DG]
  (or arXiv:0710.1305v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.1305
Journal reference: Journal of Geometry and Physics, vol. 58, (2008), 179-207
Related DOI: https://doi.org/10.1016/j.geomphys.2007.10.004

Submission history

From: Michael T. Anderson [view email]
[v1] Fri, 5 Oct 2007 20:05:13 UTC (39 KB)
[v2] Mon, 10 Mar 2008 13:21:04 UTC (40 KB)
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