Article contents
Quasisymmetric rigidity of Sierpiński carpets
$\boldsymbol{F}_{\boldsymbol{n},\boldsymbol{p}}$
Published online by Cambridge University Press: 04 June 2014
Abstract
We study a new class of square Sierpiński carpets $F_{n,p}$ (
$5\leq n,1\leq p<(n/2)-1$) on
$\mathbb{S}^{2}$, which are not quasisymmetrically equivalent to the standard Sierpiński carpets. We prove that the group of quasisymmetric self-maps of each
$F_{n,p}$ is the Euclidean isometry group of
$F_{n,p}$. We also establish that
$F_{n,p}$ and
$F_{n^{\prime },p^{\prime }}$ are quasisymmetrically equivalent if and only if
$(n,p)=(n^{\prime },p^{\prime })$.
- Type
- Research Article
- Information
- Copyright
- © Cambridge University Press, 2014
References
- 5
- Cited by