Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 81-99
University of Cincinnati, Raymond Walters College
9555 Plainfield Road, Cincinnati, Ohio 45236, U.S.A.; david.freeman 'at' uc.edu
Abstract. We prove that an unbounded L-bilipschitz homogeneous Jordan curve in the plane is of B-bounded turning, where B depends only on L. Using this result, we construct a catalogue of snowflake-type curves that includes all unbounded bilipschitz homogeneous Jordan curves, up to bilipschitz self maps of the plane. This catalogue yields characterizations of such curves in terms of certain quasiconformal maps.
2000 Mathematics Subject Classification: Primary 30C62.
Key words: Bilipschitz homogeneous, fractals, bounded turning, quasiconformal mapping.
Reference to this article: D.M. Freeman: Unbounded bilipschitz homogeneous Jordan curves. Ann. Acad. Sci. Fenn. Math. 36 (2011), 81-99.
doi:10.5186/aasfm.2011.3605
Copyright © 2011 by Academia Scientiarum Fennica