Unique continuation results for Ricci curvature and applications

Details Unique continuation results for Ricci curvature and applications Unique continuation results for Ricci curvature and applications

2007-10-05

arxiv.org/abs/0710.1305v2

Journal of Geometry and Physics, vol. 58, (2008), 179-207

Mathematics

Differential Geometry

32 pages, supercedes math.DG/0501067; final published version

Scientific paper

10.1016/j.geomphys.2007.10.004

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.

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