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Conformal Geometry and Dynamics

ISSN 1088-4173

 

 

Rotation estimates and spirals


Authors: Vladimir Gutlyanskii and Olli Martio
Journal: Conform. Geom. Dyn. 5 (2001), 6-20
MSC (2000): Primary 30C62, 30C65
DOI: https://doi.org/10.1090/S1088-4173-01-00060-1
Published electronically: March 30, 2001
MathSciNet review: 1836404
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Abstract:

It is shown that the logarithmic spiral gives the extremum to F. John's angle distortion problem for plane bilipschitz mappings. The problem of factoring spiral-like mappings into a composition of homeomorphisms with smaller isometric distortion is studied. A space counterpart of the Freedman and He theorem is obtained.


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Additional Information

Vladimir Gutlyanskii
Affiliation: Institute of Applied Mathematics and Mechanics, NAS of Ukraine, ul. Roze Luxemburg 74, 340114, Donetsk, Ukraine
Email: gut@iamm.ac.donetsk.ua

Olli Martio
Affiliation: Department of Mathematics, P. O. Box 4 (Yliopistonkatu 5), FIN-00014 University of Helsinki, Finland
Email: martio@cc.helsinki.fi

DOI: https://doi.org/10.1090/S1088-4173-01-00060-1
Received by editor(s): March 17, 2000
Received by editor(s) in revised form: January 4, 2001
Published electronically: March 30, 2001
Additional Notes: The authors thank the Mittag-Leffler Institute for financial support during the fall of the academic year 1999/2000
Article copyright: © Copyright 2001 American Mathematical Society