Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sets of Minimal Capacity and Extremal Domains   Let f be a function meromorphic in a neighborhood of infinity. The central
problem in the present investigation is to find the largest domain D \subset C
to which the function f can be extended in a meromorphic and singlevalued
manner. 'Large' means here that the complement C\D is minimal with respect to
(logarithmic) capacity. Such extremal domains play an important role in Pad'e
approximation. In the paper a unique existence theorem for extremal domains and
their complementary sets of minimal capacity is proved. The topological
structure of sets of minimal capacity is studied, and analytic tools for their
characterization are presented; most notable are here quadratic differentials
and a specific symmetry property of the Green function in the extremal domain.
A local condition for the minimality of the capacity is formulated and studied.
Geometric estimates for sets of minimal capacity are given. Basic ideas are
illustrated by several concrete examples, which are also used in a discussion
of the principal differences between the extremality problem under
investigation and some classical problems from geometric function theory that
possess many similarities, which for instance is the case for Chebotarev's
Problem.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol