Quasicircles and bounded turning circles modulo bi-Lipschitz maps

被引：15

作者：

Herron, David A. ^{[1
]}

Meyer, Daniel ^{[2
]}

机构：

[1] Univ Cincinnati, Dept Math, Cincinnati, OH 45221 USA

[2] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2012年 / 28卷 / 03期

基金：

芬兰科学院;

关键词：

Quasicircle; Jordan curve; bounded turning; doubling; ARCS;

D O I：

10.4171/RMI/687

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a catalog, of snowflake type metric circles, that describes all metric quasicircles up to bi-Lipschitz equivalence. This is a metric space analog of a result due to Rohde. Our construction also works for all bounded turning metric circles; these need not be doubling. As a byproduct, we show that a metric quasicircle with Assouad dimension strictly less than two is bi-Lipschitz equivalent to a planar quasicircle.

引用

页码：603 / 630

页数：28

共 22 条

[1] QUASICONFORMAL REFLECTIONS [J].

AHLFORS, LV .

ACTA MATHEMATICA, 1963, 109 (3-4) :291-301

[2]

[Anonymous], LECT ANAL METRIC SPA

[3]

Assouad P., 1979, C. R. Acad. Sci. Paris Ser. A-B, V288, pA731

[4] THE BOUNDARY CORRESPONDENCE UNDER QUASICON-FORMAL MAPPINGS [J].

BEURLING, A ;

AHLFORS, L .

ACTA MATHEMATICA, 1956, 96 (1-2) :125-142

[5]

Bonk M, 2001, J REINE ANGEW MATH, V541, P117

[6] INJECTIVITY OF LOCAL QUASI-ISOMETRIES [J].

GEHRING, FW .

COMMENTARII MATHEMATICI HELVETICI, 1982, 57 (02) :202-220

[7]

Luukkainen J., 1998, J. Korean Math. Soc., V35, P23

[8]

Menger K, 1930, MATH ANN, V103, P466, DOI 10.1007/BF01455705

[9] BOUNDED TURNING CIRCLES ARE WEAK-QUASICIRCLES [J].

Meyer, Daniel .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139 (05) :1751-1761

[10]

Nakki R., 1991, Expo. Math., V9, P3

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