Unique continuation results for Ricci curvature and applications. (English) Zbl 1161.58009
Certain issues related to the boundary behavior of metrics with prescribed Ricci curvature.
Let \(M\) be a compact \((n+1)\)-dimensional manifold with compact non-empty boundary \(\partial M\) are studied.
One of the main purposes of this paper is to establish a unique continuation property at the boundary \(\partial M\) for bounded metrics or for conformally compact metrics. Next, the authors prove the following isometry extension property: continuous groups of isometries at the boundary extend to isometries in the interior of complete conformally compact Einstein metrics. Connections with the constraint equations induced by the Gauss-Codazzi equations are also made in the paper.
Let \(M\) be a compact \((n+1)\)-dimensional manifold with compact non-empty boundary \(\partial M\) are studied.
One of the main purposes of this paper is to establish a unique continuation property at the boundary \(\partial M\) for bounded metrics or for conformally compact metrics. Next, the authors prove the following isometry extension property: continuous groups of isometries at the boundary extend to isometries in the interior of complete conformally compact Einstein metrics. Connections with the constraint equations induced by the Gauss-Codazzi equations are also made in the paper.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
MSC:
| 58J32 | Boundary value problems on manifolds |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 58D17 | Manifolds of metrics (especially Riemannian) |
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
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