Conformal Geometry and Dynamics

Author(s): Ole Jacob Broch
Journal: Conform. Geom. Dyn. 11 (2007), 12-28.
MSC (2000): Primary 30C20; Secondary 30C99
Posted: March 1, 2007
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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

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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Retrieve articles in Conformal Geometry and Dynamics with MSC (2000): 30C20, 30C99

Ole Jacob Broch
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Email: olejacb@math.ntnu.no

DOI: 10.1090/S1088-4173-07-00158-0
PII: S 1088-4173(07)00158-0
Keywords: John domain, reflection, hyperbolic geodesic
Received by editor(s): August 24, 2006
Posted: March 1, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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