Abstract
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 Chang-Ge [15]. In the second part of the paper, as applications, we derive some further compactness results under the perturbation condition when the L2 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 Graham-Lee [31].
Original language | English (US) |
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Article number | 107325 |
Journal | Advances in Mathematics |
Volume | 373 |
DOIs | |
State | Published - Oct 28 2020 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Compactness
- Conformally compact Einstein manifold
- Uniqueness