Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete K\"ahler-Einstein metric on Stein manifolds with negative
  curvature   We show the existence of complete negative K\"ahler-Einstein metric on Stein
manifolds with negatively pinched holomorphic sectional curvature. We prove
that any K\"ahler metrics on such manifolds can be deformed to the complete
negative K\"ahler-Einstein metric using the normalized K\"ahler-Ricci flow.

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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: hep-lat