Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Calabi-Yau problem for Riemann surfaces with finite genus and
  countably many ends   In this paper, we show that if $R$ is a compact Riemann surface and
$M=R\setminus\,\bigcup_i D_i$ is a domain in $R$ whose complement is a union of
countably many pairwise disjoint smoothly bounded closed discs $D_i$, then $M$
is the complex structure of a complete bounded minimal surface in $\mathbb
R^3$. We prove that there is a complete conformal minimal immersion
$X:M\to\mathbb R^3$ extending to a continuous map $X:\overline M\to\mathbb R^3$
such that $X(bM)=\bigcup_i X(bD_i)$ is a union of pairwise disjoint Jordan
curves. This extends a recent result for bordered Riemann surfaces.

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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: eess