A central set of dimension 2

被引：7

作者：

Bishop, Christopher J. ^{[1
]}

Hakobyan, Hrant

机构：

[1] SUNY Stony Brook, Dept Math, Stony Brook, NY 11790 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 07期

关键词：

Hausdorff dimension; central set; medial axis; skeleton; Lipschitz domain; maximal discs; disc trees;

D O I：

10.1090/S0002-9939-08-09173-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2453 / 2461

页数：9

共 8 条

[1] BISHOP CJ, 2006, CONFORMAL MAPPING LI
[2] FREE-BOUNDARY FOR ELASTIC-PLASTIC TORSION PROBLEMS
CAFFARELLI, LA
FRIEDMAN, A
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 252 (AUG) : 65 - 97
[3] Mathematical theory of medial axis transform
Choi, HI
Choi, SW
Moon, HP
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1997, 181 (01) : 57 - 88
[4] SOME REMARKS ON THE MEASURABILITY OF CERTAIN SETS
ERDOS, P
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1945, 51 (10) : 728 - 731
[5] EVANS WD, 1987, P LOND MATH SOC, V54, P141
[6] Skeletons and central sets
Fremlin, DH
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1997, 74 : 701 - 720
[7] MATTILA P, 2006, CAMBRIDGE STUDIES AD, V55
[8] TING TW, 1966, J MATH MECH, V15, P15

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