JournalsggdOnline First11 August 2022

Comparison theorems for closed geodesics on negatively curved surfaces

  • Stephen Cantrell

    University of Chicago, USA
  • Mark Pollicott

    University of Warwick, Coventry, UK
Comparison theorems for closed geodesics on negatively curved surfaces cover
Download PDF

A subscription is required to access this article.

Abstract

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 Sharp and the second author (1998). Finally, we relate our results to a recent work of Gekhtman, Taylor, and Tiozzo (2019).

Cite this article

Stephen Cantrell, Mark Pollicott, Comparison theorems for closed geodesics on negatively curved surfaces. Groups Geom. Dyn. (2022), published online first

DOI 10.4171/GGD/671