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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
MathSciNet review:
2390513
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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  .
References:
-
- 1.
- C. J. Bishop, Conformal mapping in linear time, preprint, 2006.
- 2.
- L.A. Caffarelli, A. Friedman, The free boundary for elastic-plastic torsion problems, Trans. Amer. Math. Soc. 252 (1979), 65-97. MR 534111 (80i:35059)
- 3.
- H. I. Choi, S. W. Choi and H. P. Moon. Mathematical theory of medial axis transform, Pacific J. Math. (1) 181 (1997), 57-88. MR 1491036 (99m:53008)
- 4.
- P. Erdős, Some remarks on measurability of certain sets, Bull. Amer. Math. Soc. 51 (1945), 728-731. MR 0013776 (7:197f)
- 5.
- W. D. Evans, D. J. Harris, Sobolev embeddings for generalized ridged domains, Proc. London Math. Soc. (3) 54 (1987), 141-175. MR 872254 (88b:46056)
- 6.
- D. H. Fremlin, Skeletons and central sets, Proc. London Math. Soc. (3) 74 (1997), no. 3, 701-720. MR 1434446 (97m:54059)
- 7.
- P. Mattila, Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995. MR 1333890 (96h:28006)
- 8.
- T. W. Ting, The ridge of a Jordan domain and completely plastic torsion, J. Math. Mech. 15 (1966), 15-47. MR 0184503 (32:1975)
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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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