Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An optimal systolic inequality for CAT(0) metrics in genus two   We prove an optimal systolic inequality for CAT(0) metrics on a genus~2
surface. We use a Voronoi cell technique, introduced by C.~Bavard in the
hyperbolic context. The equality is saturated by a flat singular metric in the
conformal class defined by the smooth completion of the curve y^2=x^5-x. Thus,
among all CAT(0) metrics, the one with the best systolic ratio is composed of
six flat regular octagons centered at the Weierstrass points of the Bolza
surface.

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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: chem-ph