Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Doubling Constant Mean Curvature Tori in the 3-Sphere   The Clifford tori in the 3-sphere are a one-parameter family of flat,
two-dimensional, constant mean curvature (CMC) surfaces. This paper
demonstrates that new, topologically non-trivial CMC surfaces resembling a pair
of neighbouring Clifford tori connected at a sub-lattice consisting of at least
two points by small catenoidal bridges can be constructed by perturbative PDE
methods. That is, one can create an approximate solution by gluing a rescaled
catenoid into the neighbourhood of each sub-lattice point; and then one can
show that a perturbation of this approximate submanifold exists which satisfies
the CMC condition.

18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat