Fractal tiles and quasidisks

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• 作者：Da-Wen Deng (1)
  Sze-Man Ngai (2) (3)
  
  1. School of Mathematics and Computational Sciences ; Xiangtan University ; Xiangtan ; 411105 ; Hunan ; People鈥檚 Republic of China
  2. Department of Mathematical Sciences ; Georgia Southern University ; Statesboro ; GA ; 30460-8093 ; USA
  3. College of Mathematics and Computer Science ; Hunan Normal University ; Changsha ; 410081 ; Hunan ; China
  
• 关键词：Quasidisk ; John domain ; Linearly connected domain ; Self ; similar tile ; Self ; affine tile ; Primary 52C20 ; 30C20 ; 30C62 ; Secondary 28A80
• 刊名：Mathematische Zeitschrift
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：279
• 期：1-2
• 页码：359-387
• 全文大小：1,006 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1823

文摘

We show that the interiors of a large class of planar disklike self-similar tiles are quasidisks. We also show that in general, the interior of a disklike self-affine tile may not be a John domain and thus may not be a quasidisk.