Compactness of conformally compact Einstein 4-manifolds. II. (English) Zbl 1447.53043
Summary: In this paper, we establish a number of compactness results for some class of conformally compact Einstein 4-manifolds. In the first part of the paper, we improve the earlier compactness results obtained by S.-Y. A. Chang and Y. Ge [Adv. Math. 340, 588–652 (2018; Zbl 1443.53027)]. In the second part of the paper, as applications, we derive some further compactness results under the perturbation condition when the \(L^2\) norm of the Weyl curvature is small. We also derive the global uniqueness of conformally compact Einstein metrics on the 4-ball constructed in the earlier work of C. R. Graham and J. M. Lee [Adv. Math. 87, No. 2, 186–225 (1991; Zbl 0765.53034)].
MSC:
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C18 | Conformal structures on manifolds |
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