IJPAM: Volume 34, No. 4 (2007)

HYPERBOLIC GEODESICS IN QUASIDISKS

Yuming Chu$^1$, Gendi Wang$^2$, Xiaohui Zhang$^3$
$^{1,2,3}$Department of Mathematics
Huzhou Teachers College,
Zhejiang, Huzhou, 313000, P.R. CHINA
$^1$e-mail: chuyuming@hutc.zj.cn


Abstract.Let $D$ be a Jordan proper subdomain of $R^2$ whose boundary contains at least three points, $D^*=\overline
R^2\setminus\overline D$, the exterior of $D$. In this paper, the authors prove that $D$ is a quasidisk if and only if there exists a constant $c_0\geq1$ such that

\begin{displaymath}l(\gamma)\leq c_0\vert z_1-z_2\vert\end{displaymath}

for each hyperbolic geodesics $\gamma$ in $D$ and $D^*$ with endpoints $z_1$ and $z_2$.

Received: November 29, 2006

AMS Subject Classification: 30C62

Key Words and Phrases: quasidisk, hyperbolic geodesic, hyperbolic distance

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 4