Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of hyperbolic Riemann surfaces with large systoles   Let $S$ be a compact hyperbolic Riemann surface of genus $g \geq 2$. We call
a systole a shortest simple closed geodesic in $S$ and denote by
$\mathop{sys}(S)$ its length. Let $\mathop{msys(g)}$ be the maximal value that
$\mathop{sys}(\cdot)$ can attain among the compact Riemann surfaces of genus
$g$. We call a (globally) maximal surface $S_{max}$ a compact Riemann surface
of genus $g$ whose systole has length $\mathop{msys}(g)$. In Section 2 we use
cutting and pasting techniques to construct compact hyperbolic Riemann surfaces
with large systoles from maximal surfaces. This enables us to prove several
inequalities relating $\mathop{msys}(\cdot)$ of different genera. In Section 3
we derive similar intersystolic inequalities for non-compact hyperbolic Riemann
surfaces with cusps.

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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: stat