Quasisymmetric rigidity of square Sierpinski carpets
成果类型：
Article
署名作者：
Bonk, Mario; Merenkov, Sergei
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2013.177.2.5
发表日期：
2013
页码：
591-643
关键词：
摘要：
We prove that every quasisymmetric self-homeomorphism of the standard 1/3-Sierpinski carpet S-3 is a Euclidean isometry. For carpets in a more general family, the standard 1/p-Sierpinski carpets S-p, p >= 3 odd, we show that the groups of quasisymmetric self-maps are finite dihedral. We also establish that S-p and S-q are quasisymmetrically equivalent only if p = q. The main tool in the proof for these facts is a new invariant-a certain discrete modulus of a path family-that is preserved under quasisymmetric maps of carpets.