On uniqueness and existence of conformally compact Einstein metrics with homogeneous conformal infinity. Ⅱ

作     者：Gang Li 

作者机构：School of Mathematics Shandong University 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2024年

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

摘      要：In this paper,we show that for an Sp（k+1）-invariant metric ■ on S4k+3（k 1） close to the round metric,the conformally compact Einstein （CCE） manifold （M,g） with (S4k+3,[■]) as its conformal infinity is unique up to ***,by the result in Li et al.（2017）,g is the Graham-Lee metric (see Graham and Lee （1991）) on the unit ball B1?R4k+*** also give an a priori estimate of the Einstein metric *** a byproduct of the a priori estimates,based on the estimate and Graham-Lee and Lee’s seminal perturbation results(see Graham and Lee （1991） and Lee （2006）),we directly use the continuity method to obtain an existence result of the non-positively curved CCE metric with prescribed conformal infinity (S4k+3,[■]) when the metric■ is Sp（k+1）-*** also generalize the results to the case of conformal infinity (S15,[■]) with■ a Spin（9）-invariant metric in the appendix.