Bilipschitz homogeneous Jordan curves

Authors:
Manouchehr Ghamsari and David A. Herron

Journal:
Trans. Amer. Math. Soc. **351** (1999), 3197-3216

MSC (1991):
Primary 30C65; Secondary 28A80

DOI:
https://doi.org/10.1090/S0002-9947-99-02324-7

Published electronically:
March 29, 1999

MathSciNet review:
1608313

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Abstract | References | Similar Articles | Additional Information

Abstract: We characterize bilipschitz homogeneous Jordan curves by utilizing quasihomogeneous parameterizations. We verify that rectifiable bilipschitz homogeneous Jordan curves satisfy a chordarc condition. We exhibit numerous examples including a bilipschitz homogeneous quasicircle which has lower Hausdorff density zero. We examine homeomorphisms between Jordan curves.

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Additional Information

**Manouchehr Ghamsari**

Affiliation:
Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221

Email:
manouchehr.ghamsari@ucollege.uc.edu

**David A. Herron**

Affiliation:
Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221-0025

Email:
david.herron@math.uc.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02324-7

Keywords:
Homogeneity,
self-similarity,
bilipschitz,
bounded turning,
quasicircle,
Hausdorff measure,
quasiconformal,
fractal

Received by editor(s):
September 13, 1996

Received by editor(s) in revised form:
December 15, 1997

Published electronically:
March 29, 1999

Additional Notes:
The second author was partially supported by the Charles Phelps Taft Memorial Fund at UC

Dedicated:
Dedicated to Professor Frederick W. Gehring

Article copyright:
© Copyright 1999
American Mathematical Society