Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A systolic inequality for geodesic flows on the two-sphere   For a Riemannian metric $g$ on the two-sphere, let $\ell_{\min}(g)$ be the
length of the shortest closed geodesic and $\ell_{\max}(g)$ be the length of
the longest simple closed geodesic. We prove that if the curvature of $g$ is
positive and sufficiently pinched, then the sharp systolic inequalities \[
\ell_{\rm min}(g)^2 \leq \pi \ {\rm Area}(S^2,g) \leq \ell_{\max}(g)^2, \]
hold, and each of these two inequalities is an equality if and only if the
metric $g$ is Zoll. The first inequality answers positively a conjecture of
Babenko and Balacheff. The proof combines arguments from Riemannian and
symplectic geometry.

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The categories of this paper are: eess
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph