Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loewner's torus inequality with isosystolic defect   We show that Bonnesen's isoperimetic defect has a systolic analog for
Loewner's torus inequality. The isosystolic defect is expressed in terms of the
probabilistic variance of the conformal factor of the metric g with respect to
the flat metric of unit area in the conformal class of g.

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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int