Unique continuation results for Ricci curvature and applications

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.

arXiv comment32 pages, supercedes math.DG/0501067; final published version

References in corpus (4)

• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Scalar Curvature Rigidity for asymptotically locally hyperbolic manifolds
• Classical Boundary-value Problem in Riemannian Quantum Gravity and Taub-Bolt-anti-de Sitter Geometries
• Classical Boundary-value Problem in Riemannian Quantum Gravity and Self-dual Taub-NUT-(anti)de Sitter Geometries

Cited by in corpus (24)

• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• On boundary value problems for Einstein metrics
• On the uniqueness and global dynamics of AdS spacetimes
• On the Bartnik extension problem for the static vacuum Einstein equations
• The Cauchy problems for Einstein metrics and parallel spinors
• Kähler-Einstein fillings
• Rigidity of compact Riemannian spin Manifolds with Boundary
• Unique continuation and extensions of Killing vectors at boundaries for stationary vacuum space-times
• Desingularisation de metriques d'Einstein. II
• Investigating Off-shell Stability of Anti-de Sitter Space in String Theory
• Null Geodesics and Improved Unique Continuation for Waves in Asymptotically Anti-de Sitter Spacetimes
• The bulk-boundary correspondence for the Einstein equations in asymptotically Anti-de Sitter spacetimes
• Extension of symmetries on Einstein manifolds with boundary
• A remark on the rigidity of conformally compact Poincar{é}-Einstein manifolds
• The Near-Boundary Geometry of Einstein-Vacuum Asymptotically Anti-de Sitter Spacetimes
• Local rigidity of surfaces in space forms
• Conformal harmonic coordinates
• The Dirichlet Problem for the Prescribed Ricci Curvature Equation on Cohomogeneity One Manifolds
• Null infinity and extremal horizons in AdS-CFT
• On the structure of conformally compact Einstein metrics
• On the local rigidity of Einstein manifolds with convex boundary
• Alexandrov immersions, holonomy and minimal surfaces in $S^3$
• Static vacuum Einstein metrics on bounded domains
• Metrics with Prescribed Ricci Curvature near the Boundary of a Manifold