Conformal compactification of asymptotically locally hyperbolic metrics. (English) Zbl 1259.53038
The authors extend the result of the first author [Pac. J. Math. 239, No. 2, 231–249 (2009; Zbl 1163.53025)] in order to give complete explanation of how the rate of curvature decay influences the regularity of the conformal compactification of the metric. In the second part of the work, the Einstein case is studied in detail. The authors strengthened their results significantly. In particular, using harmonic charts, they prove that the estimate on the sectional curvature implies control of all covariant derivations of the Weyl tensor.
Reviewer: Vyacheslav S. Kalnitsky (St. Peterburg)
MSC:
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 58E10 | Variational problems in applications to the theory of geodesics (problems in one independent variable) |
| 58J05 | Elliptic equations on manifolds, general theory |
Keywords:
asymptotically hyperbolic metrics; Einstein metrics; conformally compact metrics; boundary regularity; geodesic compactificationCitations:
Zbl 1163.53025References:
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