Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher genus minimal surfaces in $S^3$ and stable bundles   We consider compact minimal surfaces $f\colon M\to S^3$ of genus 2 which are
homotopic to an embedding. We assume that the associated holomorphic bundle is
stable. We prove that these surfaces can be constructed from a globally defined
family of meromorphic connections by the DPW method. The poles of the
meromorphic connections are at the Weierstrass points of the Riemann surface of
order at most 2. For the existence proof of the DPW potential we give a
characterization of stable extensions $0\to S^{-1}\to V\to S\to 0$ of spin
bundles $S$ by its dual $S^{-1}$ in terms of an associated element of $P
H^0(M;K^2).$ We also consider the family of holomorphic structures associated
to a minimal surface in $S^3.$ For surfaces of genus $g\geq2$ the holonomy of
the connections is generically non-abelian and therefore the holomorphic
structures are generically stable.

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The categories of this paper are: cs
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: physics
13
The categories of this paper are: quant-ph