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A central set of dimension 
Author(s):
Christopher
J.
Bishop;
Hrant
Hakobyan
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2453-2461.
MSC (2000):
Primary 28A78;
Secondary 28A75
Posted:
March 7, 2008
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Abstract:
The central set of a domain  is the set of centers of maximal discs in  . Fremlin proved that the central set of a planar domain has zero area and asked whether it can have Hausdorff dimension strictly larger than  . We construct a planar domain with central set of Hausdorff dimension  .
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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:
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
Posted:
March 7, 2008
Additional Notes:
The first author was partially supported by NSF Grant DMS 04-05578.
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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