Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Uniqueness And Existence of Conformally Compact Einstein Metrics with
  Homogeneous Conformal Infinity. II   In this paper we show that for an $\text{Sp}(k+1)$ invariant metric $\hat{g}$
on $\mathbb{S}^{4k+3}$ $(k\geq 1)$ 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 $B_1\subset
\mathbb{R}^{4k+4}$. 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. We also generalize the results to the case of
conformal infinity $(\mathbb{S}^{15},[\hat{g}])$ with $\hat{g}$ a
Spin$(9)$-invariant metric in the appendix.

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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol