Note on quasisymmetric rigidity of carpets

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-05-21 DOI:10.1016/j.topol.2024.108960

Yahui Sheng , Chun Wei , Fan Wen

引用次数: 0

Abstract

We prove in a constructive way that, given $α > 1$ , there exists a quasisymmetrically rigid metric carpet of Hausdorff dimension >α and whose peripheral circles are all rectifiable.

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关于地毯准对称刚性的说明

我们用一种建设性的方法证明，在给定 α>1 的情况下，存在一个豪斯多夫维度为 >α的准对称刚性度量地毯，其外围圆都是可矫正的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.