On Brunn–Minkowski-Type Inequalities for Polar Bodies

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• 作者：María A. Hernández Cifre ; Jesús Yepes Nicolás
• 关键词：Brunn–Minkowski inequality ; Polar body ; Firey addition ; Rogers–Shephard inequality ; Primary 52A20 ; 52A40 ; Secondary 52A39
• 刊名：Journal of Geometric Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：26
• 期：1
• 页码：143-155
• 全文大小：417 KB
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• 作者单位：María A. Hernández Cifre (1)
  Jesús Yepes Nicolás (1)
  
  1. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Murcia, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

In this paper we prove a Brunn–Minkowski-type inequality for the polar set of the \(p\)-sum of convex bodies, which generalizes previous results by Firey, and we show it has an equivalent multiplicative version. We also make some considerations for the polar set of the so-called difference body. Keywords Brunn–Minkowski inequality Polar body Firey addition Rogers–Shephard inequality