A generalization of domains of constant width

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• 作者：Deyan Zhang
• 关键词：Convex domain ; Constant width ; Diameter ; Equiangular polygon ; Higher order width ; Perimeter ; 52A38 ; 52A40
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：57
• 期：1
• 页码：259-270
• 全文大小：439 KB
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• 作者单位：Deyan Zhang (1) (2)
  
  1. Department of Mathematics, Tongji University, Shanghai, 200092, People’s Republic of China
  2. College of mathematics and statistics, Hexi University, Zhangye, 734000, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra
  Convex and Discrete Geometry
  Geometry
  Algebraic Geometry
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2191-0383

文摘

Recently, Ou and Pan introduced the higher order width functions of convex domains, and posed a generalization of the Blaschke–Lebesgue problem: among all convex domains having constant \(k\)-order width, which has the least possible area. In this paper, we continue to study convex domains having constant \(k\)-order width and obtain some characterizations of this class of sets, which are slightly different from those of constant width convex domains. Keywords Convex domain Constant width Diameter Equiangular polygon Higher order width Perimeter