Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An elementary proof for the Double Bubble problem in $\ell^1$ norm   We study the double bubble problem with perimeter taken with respect to the
$\ell_1$ norm on $\mathbb{R}^2$. We give an elementary proof for the existence
of minimizing sets for any volume ratio parameter $0<\alpha\le1$ by direct
comparison to a small family of parameterized sets. By simple analysis on this
family we obtain the minimizing shapes found in Morgan et al 1998.

13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio