Unique continuation results for Ricci curvature and applications |
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Authors: | Michael T Anderson Marc Herzlich |
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Institution: | 1. Department of Mathematics, S.U.N.Y. at Stony Brook, Stony Brook, NY 11794-3651, USA;2. Institut de mathématiques et de modélisation de Montpellier, CNRS et Université Montpellier II, 34095 Montpellier Cedex 5, France |
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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 on such manifolds. 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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Keywords: | 58J32 58J60 53C21 |
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