Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformation of Einstein metrics and $L^2$ cohomology on strictly
  pseudoconvex domains   We construct new complete Einstein metrics on smoothly bounded strictly
pseudoconvex domains in Stein manifolds. This is done by deforming the
K\"ahler-Einstein metric of Cheng and Yau, the approach that generalizes the
works of Roth and Biquard on the deformations of the complex hyperbolic metric
on the unit ball. Recasting the problem into the question of vanishing of an
$L^2$ cohomology and taking advantage of the asymptotic complex hyperbolicity
of the Cheng-Yau metric, we establish the possibility of such a deformation
when the dimension of the domain is larger than or equal to three.

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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
16
The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol