Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An end-to-end construction of doubly periodic minimal surfaces   Using Traizet's regeneration method, we prove that for each positive integer
n there is a family of embedded, doubly periodic minimal surfaces with parallel
ends in Euclidean space of genus 2n-1 and 4 ends in the quotient by the maximal
group of translations. The genus 2n-1 family converges smoothly to 2n copies of
Scherk's doubly periodic minimal surface. The only previously known doubly
periodic minimal surfaces with parallel ends and genus greater than 3 limit in
a foliation of Euclidean space by parallel planes.

36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con