Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds
In this paper, we establish compactness results for some classes of conformally compact Einstein metrics defined on manifolds of dimension d ≥ 4. In the special case when the manifold is the Euclidean ball with the unit sphere as the conformal infinity, the existence of such class of metrics has bee...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-03-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2023-0124 |
| _version_ | 1797219164005335040 |
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| author | Chang Sun-Yung Alice Ge Yuxin Jin Xiaoshang Qing Jie |
| author_facet | Chang Sun-Yung Alice Ge Yuxin Jin Xiaoshang Qing Jie |
| author_sort | Chang Sun-Yung Alice |
| collection | DOAJ |
| description | In this paper, we establish compactness results for some classes of conformally compact Einstein metrics defined on manifolds of dimension d ≥ 4. In the special case when the manifold is the Euclidean ball with the unit sphere as the conformal infinity, the existence of such class of metrics has been established in the earlier work of C. R. Graham and J. Lee (“Einstein metrics with prescribed conformal infinity on the ball,” Adv. Math., vol. 87, no. 2, pp. 186–225, 1991). As an application of our compactness result, we derive the uniqueness of the Graham–Lee metrics. As a second application, we also derive some gap theorem, or equivalently, some results of non-existence CCE fill-ins. |
| first_indexed | 2024-04-24T12:29:17Z |
| format | Article |
| id | doaj.art-1ce19b95b1b44ad0a3b2735e169fb8c1 |
| institution | Directory Open Access Journal |
| issn | 2169-0375 |
| language | English |
| last_indexed | 2024-04-24T12:29:17Z |
| publishDate | 2024-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-1ce19b95b1b44ad0a3b2735e169fb8c12024-04-08T07:35:25ZengDe GruyterAdvanced Nonlinear Studies2169-03752024-03-0124124727810.1515/ans-2023-0124Perturbation compactness and uniqueness for a class of conformally compact Einstein manifoldsChang Sun-Yung Alice0Ge Yuxin1Jin Xiaoshang2Qing Jie3Department of Mathematics, Princeton University, Princeton, NJ08544, USAIMT, Université Toulouse 3, 118, Route de Narbonne 31062Toulouse, FranceSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, ChinaMathematics Department, UCSC, 1156 High Street, Santa Cruz, CA95064, USAIn this paper, we establish compactness results for some classes of conformally compact Einstein metrics defined on manifolds of dimension d ≥ 4. In the special case when the manifold is the Euclidean ball with the unit sphere as the conformal infinity, the existence of such class of metrics has been established in the earlier work of C. R. Graham and J. Lee (“Einstein metrics with prescribed conformal infinity on the ball,” Adv. Math., vol. 87, no. 2, pp. 186–225, 1991). As an application of our compactness result, we derive the uniqueness of the Graham–Lee metrics. As a second application, we also derive some gap theorem, or equivalently, some results of non-existence CCE fill-ins.https://doi.org/10.1515/ans-2023-012453c1853c2558j60 |
| spellingShingle | Chang Sun-Yung Alice Ge Yuxin Jin Xiaoshang Qing Jie Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds Advanced Nonlinear Studies 53c18 53c25 58j60 |
| title | Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds |
| title_full | Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds |
| title_fullStr | Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds |
| title_full_unstemmed | Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds |
| title_short | Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds |
| title_sort | perturbation compactness and uniqueness for a class of conformally compact einstein manifolds |
| topic | 53c18 53c25 58j60 |
| url | https://doi.org/10.1515/ans-2023-0124 |
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