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Bi-Lipschitz homogeneous curves in  are quasicircles
Author(s):
Christopher
J.
Bishop
Journal:
Trans. Amer. Math. Soc.
353
(2001),
2655-2663.
MSC (2000):
Primary 30C65
Posted:
March 14, 2001
MathSciNet review:
1828465
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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.
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Additional Information:
Christopher
J.
Bishop
Affiliation:
Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
Email:
bishop@math.sunysb.edu
DOI:
10.1090/S0002-9947-01-02755-6
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
Posted:
March 14, 2001
Additional Notes:
The author is partially supported by NSF Grant DMS 98-00924
Copyright of article:
Copyright
2001,
American Mathematical Society
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