IJPAM: Volume 39, No. 1 (2007)

AN IMPROVEMENT OF MORI'S CONSTANT IN
THE THEORY OF SPACE QUASICONFORMAL MAPPINGS

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


Abstract.Let $A(n,K)=${$f~\big\vert~f$ is a $K$-quasiconformal mapping which maps unit ball $B^n$ onto $B^n$ with $f(0)=0$}, and

\begin{displaymath}M(n,K)=\sup_{f\in A(n,K)\atop x,y\in\overline B^n,x\neq y}\fr... ...)\vert}{\vert y-x\vert^\alpha}, \qquad \alpha=K^{\frac1{1-n}}.\end{displaymath}

In this paper, the authors prove that $M(n,K)\leq2\lambda_n^{1-\alpha}m^{\alpha}<3\lambda_n^2$, where $m=\frac{1+\{1+[1+(\frac32)^\beta\lambda_n^{1+\beta}]^2\}^{\frac12}}2$, $\beta=\frac1\alpha$, and $\lambda_n\in[4,2e^{n-1}]$ is the Grötzsch ring constant of $R^n$.

Received: April 24, 2007

AMS Subject Classification: 30C65

Key Words and Phrases: Grötzsch ring, Teichmüller ring, quasiconformal mapping, Mori's constant

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 1