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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: March 29, 1999
MathSciNet review: 1608313
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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: http://dx.doi.org/10.1090/S0002-9947-99-02324-7
PII: S 0002-9947(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