Bi-Kipschitz homogeneous curves in R-2 are quasicircles

Authors
Bishop, CJ
Citation
Cj. Bishop, Bi-Kipschitz homogeneous curves in R-2 are quasicircles, T AM MATH S, 353(7), 2001, pp. 2655-2663
Citations number
15
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
353
Issue
7
Year of publication
2001
Pages
2655 - 2663
Database
ISI
SICI code
0002-9947(2001)353:7<2655:BHCIRA>2.0.ZU;2-U
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. Co mbined with results of Herron and Mayer this gives several characterization s of such curves in the plane.