•  
  •  
 

Turkish Journal of Mathematics

DOI

10.3906/mat-1808-101

Abstract

Let $\xi$ and $\eta$ be two noncommuting isometries of the hyperbolic $3$-space $\mathbb{H}^3$ so that $\Gamma=\langle\xi,\eta\rangle$ is a purely loxodromic free Kleinian group. For $\gamma\in\Gamma$ and $z\in\hyp$, let $d_{\gamma}z$ denote the hyperbolic distance between $z$ and $\gamma(z)$. Let $z_1$ and $z_2$ be the midpoints of the shortest geodesic segments connecting the axis of $\xi$ to the axes of $\eta\xi\eta^{-1}$ and $\eta^{-1}\xi\eta$, respectively. In this manuscript, it is proved that if $d_{\gamma}z_2

First Page

833

Last Page

861

Included in

Mathematics Commons

Share

COinS