Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds

Sun Yung Alice Chang, Yuxin Ge, Xiaoshang Jin, Jie Qing

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)247-278
Number of pages32
JournalAdvanced Nonlinear Studies
Volume24
Issue number1
DOIs
StatePublished - Feb 1 2024

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Mathematics

Keywords

  • 53C18
  • 53C25
  • 58J60

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