On the minimal distance between elliptic fixed points for geometrically-finite Fuchsian groups

TL;DR

This paper establishes a lower bound on the minimal hyperbolic distance between elliptic fixed points of geometrically-finite Fuchsian groups, depending on a universal constant and the shortest closed geodesic length.

Contribution

It provides a new lower bound on the distance between elliptic fixed points in geometrically-finite Fuchsian groups, linking it to geometric invariants.

Findings

Lower bound on elliptic fixed points distance established

Bound depends on universal constant and shortest geodesic length

Enhances understanding of geometric structure of Fuchsian groups

Abstract

Let $\Gamma$ be a geometrically-finite Fuchsian group acting on the upper half plane $\hh.$ Let $\E$ denote the set of elliptic fixed points of $\Gamma$ in $\hh.$ We give a lower bound on the minimal hyperbolic distance between points in $\E.$ Our bound depends on a universal constant and the length of the smallest closed geodesic on $\Gamma \backslash \hh.$