Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit of Karcher's Saddle towers   In 1988, Karcher generalized the family of singly periodic Scherk minimal
surfaces by constructing, for each natural $n\geq 2$, a $(2n-3)$-parameter
family of singly periodic minimal surfaces with genus zero and $2n$ Scherk-type
ends in the quotient, called {\it saddle towers}. They have been recently
classified by P\'erez and Traizet \cite{PeTra1} as the only properly embedded
singly periodic minimal surfaces in $\R^3$ with genus zero and finitely many
Scherk-type ends in the quotient. In this paper we obtain as a limit of saddle
towers: the catenoid; the doubly periodic Scherk minimal surface of angle
$\frac{\pi}{2}$; any singly periodic Scherk minimal surface; or a KMR example
of the kind $M_{\t,\a,0}$ (also called {\it toroidal halfplane layer}, see
\cite{ka4,mrod1}), which are doubly periodic minimal surfaces with parallel
ends and genus one in the quotient; or one of the examples constructed in
\cite{mrt}, which are singly periodic minimal surfaces with genus zero and one
limit end in the quotient by all their periods.

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The categories of this paper are: solv-int
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
12
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: dg-ga
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The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an