Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comparison theorems for closed geodesics on negatively curved surfaces   In this note we present new asymptotic estimates comparing the word length
and geodesic length of closed geodesics on surfaces with (variable) negative
sectional curvatures. In particular, we provide an averaged comparison of these
two important quantities and obtain precise statistical results, including a
central limit theorem and a local limit theorem. Further, as a corollary we
also improve an asymptotic formula of R. Sharp and the second author. Finally,
we relate our results to recent work of Gekhtman, Taylor and Tiozzo.

22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th