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- W2784890224 abstract "In this paper we show that for an $text{Sp}(k+1)$ invariant metric $hat{g}$ on $mathbb{S}^{4k+3}$ $(kgeq 1)$ close to the round metric, the conformally compact Einstein (CCE) manifold $(M, g)$ with $(mathbb{S}^{4k+3}, [hat{g}])$ as its conformal infinity is unique up to isometries. Moreover, by the result in [LiQingShi], $g$ is the Graham-Lee metric on the unit ball $B_1subset mathbb{R}^{4k+4}$. We also give an a priori estimate on the Einstein metric $g$. Based on the estimate and Graham-Lee and Lee's seminal perturbation result, we use the continuity method directly to obtain an existence result of the non-positively curved CCE metric with prescribed conformal infinity $(mathbb{S}^{4k+3}, [hat{g}])$ when the metric $hat{g}$ is $text{Sp}(k+1)$-invariant." @default.
- W2784890224 created "2018-02-02" @default.
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- W2784890224 date "2018-01-24" @default.
- W2784890224 modified "2023-09-27" @default.
- W2784890224 title "On Uniqueness And Existence of Conformally Compact Einstein Metrics with Homogeneous Conformal Infinity. II" @default.
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