Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degree and holomorphic extensions   Let D be a bounded convex domain in C^N, N\geq 2. We prove that a continous
map F from bD to C^N extends holomorphically through D if and only if for every
polynomial map P from C^N to C^N such that F+P has no zero on bD, the degree of
F+P|bD is nonnegative. We also prove another such theorem for more general
domains.

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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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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: funct-an
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The categories of this paper are: atom-ph