Bi-lipschitz homogeneous curves in ℝ2 are quasicircles

Christopher J. Bishop

doi:10.1090/s0002-9947-01-02755-6

Bi-lipschitz homogeneous curves in ℝ² are quasicircles

Christopher J. Bishop

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We show that a bi-Lipschitz homogeneous curve in the plane must satisfy the bounded turning condition, and that this is false in higher dimensions. Combined with results of Herron and Mayer this gives several characterizations of such curves in the plane.

Original language	English
Pages (from-to)	2655-2663
Number of pages	9
Journal	Transactions of the American Mathematical Society
Volume	353
Issue number	7
DOIs	https://doi.org/10.1090/s0002-9947-01-02755-6
State	Published - 2001

Keywords

Bi-Lipschitz mappings
Chord-arc
Hausdorff dimension.
Homogeneous continua
Quasicircles, bounded turning
Quasiconformal mappings
Quasihomogeneous embeddings

Access to Document

10.1090/s0002-9947-01-02755-6

Cite this

@article{233f9606d1764f079f70a5caff4c2b8f,

title = "Bi-lipschitz homogeneous curves in ℝ2 are quasicircles",

abstract = "We show that a bi-Lipschitz homogeneous curve in the plane must satisfy the bounded turning condition, and that this is false in higher dimensions. Combined with results of Herron and Mayer this gives several characterizations of such curves in the plane.",

keywords = "Bi-Lipschitz mappings, Chord-arc, Hausdorff dimension., Homogeneous continua, Quasicircles, bounded turning, Quasiconformal mappings, Quasihomogeneous embeddings",

author = "Bishop, \{Christopher J.\}",

year = "2001",

doi = "10.1090/s0002-9947-01-02755-6",

language = "English",

volume = "353",

pages = "2655--2663",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

number = "7",

}

TY - JOUR

T1 - Bi-lipschitz homogeneous curves in ℝ2 are quasicircles

AU - Bishop, Christopher J.

PY - 2001

Y1 - 2001

N2 - We show that a bi-Lipschitz homogeneous curve in the plane must satisfy the bounded turning condition, and that this is false in higher dimensions. Combined with results of Herron and Mayer this gives several characterizations of such curves in the plane.

AB - We show that a bi-Lipschitz homogeneous curve in the plane must satisfy the bounded turning condition, and that this is false in higher dimensions. Combined with results of Herron and Mayer this gives several characterizations of such curves in the plane.

KW - Bi-Lipschitz mappings

KW - Chord-arc

KW - Hausdorff dimension.

KW - Homogeneous continua

KW - Quasicircles, bounded turning

KW - Quasiconformal mappings

KW - Quasihomogeneous embeddings

UR - https://www.scopus.com/pages/publications/23044528395

U2 - 10.1090/s0002-9947-01-02755-6

DO - 10.1090/s0002-9947-01-02755-6

M3 - Article

AN - SCOPUS:23044528395

SN - 0002-9947

VL - 353

SP - 2655

EP - 2663

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 7

ER -

Bi-lipschitz homogeneous curves in ℝ² are quasicircles

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this