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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A central set of dimension $ 2$


Authors: Christopher J. Bishop and Hrant Hakobyan
Journal: Proc. Amer. Math. Soc. 136 (2008), 2453-2461
MSC (2000): Primary 28A78; Secondary 28A75
Published electronically: March 7, 2008
MathSciNet review: 2390513
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Abstract: The central set of a domain $ D$ is the set of centers of maximal discs in $ D$. Fremlin proved that the central set of a planar domain has zero area and asked whether it can have Hausdorff dimension strictly larger than $ 1$. We construct a planar domain with central set of Hausdorff dimension $ 2$.


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Additional Information

Christopher J. Bishop
Affiliation: Department of Mathematics, SUNY Stony Brook, Stony Brook, New York 11790
Email: bishop@math.sunysb.edu

Hrant Hakobyan
Affiliation: Department of Mathematics, University of Toronto, Toronto, ON, Canada M5S 2E4

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09173-9
PII: S 0002-9939(08)09173-9
Keywords: Hausdorff dimension, central set, medial axis, skeleton, Lipschitz domain, maximal discs, disc trees
Received by editor(s): February 1, 2007
Published electronically: March 7, 2008
Additional Notes: The first author was partially supported by NSF Grant DMS 04-05578.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.