English

Counting geodesic loops on surfaces of genus at least 2 without conjugate points

Differential Geometry 2023-09-26 v1 Dynamical Systems

Abstract

In this paper we prove asymptotic estimates for closed geodesic loops on compact surfaces with no conjugate points. These generalize the classical counting results of Huber and Margulis and sector theorems for surfaces of strictly negative curvature. We will also prove more general sector theorems, generalizing results of Nicholls and Sharp for special case of surfaces of strictly negative curvature.

Keywords

Cite

@article{arxiv.2309.14099,
  title  = {Counting geodesic loops on surfaces of genus at least 2 without conjugate points},
  author = {Mark Pollicott and Khadim War},
  journal= {arXiv preprint arXiv:2309.14099},
  year   = {2023}
}