Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Bi-Lipschitz homogeneous curves in $\mathbb{R} ^2$ are quasicircles

Author: Christopher J. Bishop
Journal: Trans. Amer. Math. Soc. 353 (2001), 2655-2663
MSC (2000): Primary 30C65
Published electronically: March 14, 2001
MathSciNet review: 1828465
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 30C65

Retrieve articles in all journals with MSC (2000): 30C65

Additional Information

Christopher J. Bishop
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651

PII: S 0002-9947(01)02755-6
Keywords: Bi-Lipschitz mappings, homogeneous continua, quasicircles, bounded turning, quasihomogeneous embeddings, chord-arc, quasiconformal mappings, Hausdorff dimension
Received by editor(s): August 12, 1999
Published electronically: March 14, 2001
Additional Notes: The author is partially supported by NSF Grant DMS 98-00924
Article copyright: © Copyright 2001 American Mathematical Society