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Conformal Geometry and Dynamics

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On reflections in Jordan curves

Author: Ole Jacob Broch
Journal: Conform. Geom. Dyn. 11 (2007), 12-28
MSC (2000): Primary 30C20; Secondary 30C99
Published electronically: March 1, 2007
MathSciNet review: 2295995
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Abstract: A purely geometric method for constructing reflections in Jordan curves on the Riemann sphere based on hyperbolic geodesics is introduced. It is then possible to investigate the relations between the geometry of a Jordan domain $D$ and the properties of the reflection by studying properties of hyperbolic geodesics. This idea is used to characterize unbounded Jordan John domains in terms of reflections satisfying a kind of Lipschitz condition.

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Additional Information

Ole Jacob Broch
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

Keywords: John domain, reflection, hyperbolic geodesic
Received by editor(s): August 24, 2006
Published electronically: March 1, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.