Closed geodesics on surfaces without conjugate points

TL;DR

This paper provides asymptotic estimates for counting free homotopy classes of closed geodesics on certain manifolds without conjugate points, specifically covering all compact surfaces of genus at least 2.

Contribution

It extends Margulis-type asymptotic counting results to a broad class of surfaces without conjugate points, a setting less explored in prior work.

Findings

Asymptotic estimates for closed geodesics on these surfaces

Results apply to all compact surfaces of genus ≥ 2 without conjugate points

Generalization of Margulis' counting results

Abstract

We obtain Margulis-type asymptotic estimates for the number of free homotopy classes of closed geodesics on certain manifolds without conjugate points. Our results cover all compact surfaces of genus at least 2 without conjugate points.