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Quasisymmetrically rigid self-similar carpets

Part of: Classical measure theory Analysis on metric spaces

Published online by Cambridge University Press:  22 October 2024

FENG RAO  and
FAN WEN Open the ORCID record for FAN WEN [Opens in a new window]
FENG RAO
Affiliation:
School of Mathematics Statistics, Hubei University of Science Technology, Xianning 437100, Hubei, China (e-mail: 601682168@qq.com)
FAN WEN*
Affiliation:
Department of Mathematics, Jinan University, Guangzhou 510632, China
*
e-mail: wenfan@jnu.edu.cn
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Abstract

We define balanced self-similar quasi-round carpets and compare the carpet moduli of some path families relating to such a carpet. Then, using some known results on quasiconformal geometry of carpets, we prove that the group of quasisymmetric self-homeomorphisms of every balanced self-similar quasi-round carpet is finite. Furthermore, we prove that some balanced self-similar carpets in the unit square with strong geometric symmetry are quasisymmetrically rigid by using the quasisymmetry of weak tangents of carpets.

Keywords

balanced self-similar quasi-round carpetquasisymmetric rigiditycarpet modulusweak tangent

MSC classification

Primary: 30L05: Geometric embeddings of metric spaces
Secondary: 28A80: Fractals 30L10: Quasiconformal mappings in metric spaces

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 45 , Issue 6 , June 2025 , pp. 1915 - 1928
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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