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
Keywords
Free Kleinian groups, Jörgensen's inequality, the $\log 3$ theorem, loxodromic isometries, hyperbolic displacements
First Page
833
Last Page
861
Recommended Citation
YÜCE, İLKER SAVAŞ
(2019)
"Jörgensen's inequality and purely loxodromic two-generator free Kleinian groups,"
Turkish Journal of Mathematics: Vol. 43:
No.
2, Article 19.
https://doi.org/10.3906/mat-1808-101
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss2/19
