Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitesimal generators and the Loewner equation on complete hyperbolic
  manifolds   We characterize infinitesimal generators on complete hyperbolic complex
manifolds without any regularity assumption on the Kobayashi distance. This
allows to prove a general Loewner type equation with regularity of any order
$d\in [1,+\infty ]$. Finally, based on these results, we focus on some open
problems naturally arising.

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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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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: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: nucl-th