Dual Orlicz geominimal surface area

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• 作者：Tongyi Ma ; Weidong Wang
• 关键词：52A30 ; 52A40 ; convex bodies ; star bodies ; dual Orlicz mixed volume ; dual Orlicz geominimal surface area
• 刊名：Journal of Inequalities and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,339 KB
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• 作者单位：Tongyi Ma (1)
  Weidong Wang (2)
  
  1. College of Mathematics and Statistics, Hexi University, Zhangye, 734000, P.R. China
  2. Department of Mathematics, China Three Gorges University, Yichang, 443002, P.R. China
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

The \(L_{p}\)-geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski theory. In this paper, based on the concept of the dual Orlicz mixed volume, we extend the dual geominimal surface area to the Orlicz version and give its properties. In addition, the isoperimetric inequality, a Blaschke-Santaló type inequality, and the monotonicity inequality for the dual Orlicz geominimal surface areas are established. Keywords convex bodies star bodies dual Orlicz mixed volume dual Orlicz geominimal surface area