2007/10/31 by Michael T. Anderson, Marc Herzlich · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.1016/j.geomphys.2007.10.004
published as Journal of Geometry and Physics, vol. 58, (2008), 179-207 · 32 pages, supercedes math.DG/0501067; final published version
openalex publication_date 2007/11/14 · arxiv created 2008/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.