Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Teichmuller theory and handle addition for minimal surfaces   We develop Teichmuller theoretical methods to construct new minimal surfaces
in $\BE^3$ by adding handles and planar ends to existing minimal surfaces in
$\BE^3$. We exhibit this method on an interesting class of minimal surfaces
which are likely to be embedded, and have a low degree Gau\ss map for their
genus; the (Weierstrass data) period problem for these surfaces is of arbitrary
dimension.
  In particular, we exhibit a two-parameter family of complete minimal surfaces
in the Euclidean three-space $\BE^3$ which generalize the breakthrough minimal
surface of C. Costa; these new surfaces are embedded (at least) outside a
compact set, and are indexed (roughly) by the number of ends they have and
their genus. They have at most eight self-symmetries despite being of
arbitrarily large genus, and are interesting for a number of reasons. Moreover,
our methods also extend to prove that some natural candidate classes of
surfaces cannot be realized as minimal surfaces in $\BE^3$. As a result of both
aspects of this work, we obtain a classification of a family of surfaces as
either realizable or unrealizable as minimal surfaces.

5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th