Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Isoperimetric Problem in a Lattice of $\mathbb{H}^3$   The isoperimetric problem is one of the oldest in geometry and it consists of
finding a surface of minimum area that encloses a given volume $V$. It is
particularly important in physics because of its strong relation with
stability, and this also involves the study of phenomena in non-Euclidean
spaces. Of course, such spaces cannot be customized for lab experiments but we
can resort to computational simulations, and one of the mostly used softwares
for this purpose is the Surface Evolver. In this paper we use it to study the
isoperimetric problem in a lattice of the three dimensional hyperbolic space.
More precisely: up to isometries, there exists a unique tesselation of
$\mathbb{H}^3$ by non-ideal cubes $\mathcal{C}$. Now let $\Omega$ be a
connected isoperimetric region inside the non-ideal hyperbolic cube
$\mathcal{C}$. Under weak assumptions on graph and symmetry we find all
numerical solutions $\Sigma=\partial\Omega$ of the isoperimetric problem in
$\mathcal{C}$.

12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
2
The categories of this paper are: math
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ