Comparison theorems for closed geodesics on negatively curved surfaces

2020/02/22 by Stephen Cantrell, Cantrell, Stephen, Mark Pollicott +1 · 1 citation
Engineering · Mathematics · #3D Shape Modeling and Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.2002.09767

openalex publication_date 2020/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 R. Sharp and the second author. Finally, we relate our results to recent work of Gekhtman, Taylor and Tiozzo.

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• A Central Limit Theorem for the Winding Number of Low-Lying Closed Geodesics

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