Determination of star bodies from p-centroid bodies

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• 作者：LUJUN GUO (1)
  GANGSONG LENG (1)
  
• 关键词：p ; centroid body ; star body ; spherical integral transformation ; p ; cosine transformation
• 刊名：Proceedings Mathematical Sciences
• 出版年：2013
• 出版时间：November 2013
• 年：2013
• 卷：123
• 期：4
• 页码：577-586
• 全文大小：217 KB
• 作者单位：LUJUN GUO (1)
  GANGSONG LENG (1)
  
  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China
  
• ISSN：0973-7685

文摘

In this paper, we prove that an origin-symmetric star body is uniquely determined by its p-centroid body. Furthermore, using spherical harmonics, we establish a result for non-symmetric star bodies. As an application, we show that there is a unique member of $\Gamma_p\langle K\rangle$ characterized by having larger volume than any other member, for all real p?≥- that are not even natural numbers, where $\Gamma_p\langle K\rangle$ denotes the p-centroid equivalence class of the star body K.