Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functionals on Closed 2-Surfaces   We show that the 2-torus in ${\mathbb R}^3$ is a critical point of a sequence
of functionals ${\cal F}_{n}$ ($n=1,2,3, \cdots$) defined over compact
2-surfaces in ${\mathbb R}^3$. When the Lagrange function ${\cal E}$ is a
polynomial of degree $n$ of the mean curvature $H$ of the surface, the radii
($a,r$) of the 2-torus are related as $\frac{a^2}{r^2}=\frac{n^2-n}{n^2-n-1}, n
\ge 2$. If the Lagrange function depends on both mean and Gaussian curvatures,
the 2- torus remains to be a critical point of ${\cal F}_{n}$ without any
constraints on the radii of the torus.

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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: econ