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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

A Cantor set with hyperbolic complement


Authors: Juan Souto and Matthew Stover
Journal: Conform. Geom. Dyn. 17 (2013), 58-67
MSC (2010): Primary 30F40, 57M50; Secondary 30F45
Published electronically: April 22, 2013
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Abstract: We construct a Cantor set in $ \mathbb{S}^3$ whose complement admits a complete hyperbolic metric.


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Additional Information

Juan Souto
Affiliation: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2
Email: jsouto@math.ubc.ca

Matthew Stover
Affiliation: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109–1043
Email: stoverm@umich.edu

DOI: http://dx.doi.org/10.1090/S1088-4173-2013-00249-X
PII: S 1088-4173(2013)00249-X
Received by editor(s): May 29, 2012
Published electronically: April 22, 2013
Additional Notes: The first author was partially supported by NSERC Discovery and Accelerator Supplement grants.
The second author was partially supported by NSF RTG grant DMS 0602191.
Dedicated: To Dick Canary on the occasion of his $50^{th}$ birthday
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.