Extension of symmetries on Einstein manifolds with boundary

Abstract

We investigate the validity of the isometry extension property for (Riemannian) Einstein metrics on manifolds with boundary. Given a metric on the boundary, this is the issue of whether any Killing field of the boundary metric extends to a Killing field of any bulk or filling Einstein metric inducing the given data on the boundary. Under a mild condition on the fundamental group, this is proved to be the case at least when the Killing field preserves the mean curvature of the boundary.

Correction to proof of main result given in new Appendix

References in corpus (4)

• On the uniqueness and global dynamics of AdS spacetimes
• Unique continuation results for Ricci curvature and applications
• Ricci-flat Metrics with U(1) Action and the Dirichlet Boundary-value Problem in Riemannian Quantum Gravity and Isoperimetric Inequalities
• Local rigidity of surfaces in space forms

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