Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature and $L^p$ Bergman spaces on complex submanifolds in ${\mathbb
  C}^N$   Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete
K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on
the $L^p$ Bergman space of holomorphic sections of a given Hermitian line
bundle $L$ over $M$ and the associated $L^2$ cohomology groups are obtained.
Some infiniteness theorems are also given in order to test the accuracy of
finiteness theorems. As applications we obtain some rigidity results concerning
growth of curvatures.

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The categories of this paper are: cs
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The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph