IJPAM: Volume 36, No. 3 (2007)

A GEOMETRIC INTERPRETATION FOR SPHERE
DISTORTION OF SURFACES IN 3-SPACE

Gong Weiming$^1$, Chu Yuming$^2$, Wu Linli$^3$
$^1$Department of Mathematics
Hunan City University
Yiyang, 413000, P.R. CHINA
e-mail: gwm@mail.hncul.net
$^{2,3}$Department of Mathematics
Huzhou Teachers College
Huzhou, 313000, P.R. CHINA
$^2$e-mail: chuyuming@hutc.zj.cn
$^3$e-mail: wll1303@hutc.zj.cn


Abstract.Let $\Sigma$ be a 2-dimensional Jordan surface in $\overline R^3$ which contains $\infty$, in this paper, the authors prove that $\Sigma$ has sphere distortion $c$ if and only if there exists a constant $b$, $2\leq b<\infty$, such that for each point $w_1$ in one component of $\overline R^3\setminus\Sigma$ there exists a point $w_2$ in the other component with $b(w_j,\Sigma)\geq\vert w_1-w_2\vert$, $j=1,2$.

Received: June 22, 2006

AMS Subject Classification: 30C99

Key Words and Phrases: sphere distortion, Möbius transformation, spherical ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 3