Centers and partial volumes of convex cones I. Basic theory

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• 作者：Alberto Seeger (1)
  Mounir Torki (2)
  
  1. D茅partement de Math茅matiques ; Universit茅 d鈥橝vignon ; 33 rue Louis Pasteur ; 84000 ; Avignon ; France
  2. Universit茅 d鈥橝vignon ; CERI ; 339 chemin de Meinajaries ; 84911 ; Avignon ; France
  
• 关键词：Partial volume of a convex cone ; Solid angle ; Volumetric center ; Incenter ; 51M25 ; 52A38 ; 47L07
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：56
• 期：1
• 页码：227-248
• 全文大小：241 KB
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• 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

We study the concept of least partial volume of a proper cone in \(\mathbb {R}^n\) . This notion is a reasonable alternative to the classical concept of solid angle. In tandem, we study the concept of volumetric center of a proper cone. We compare this kind of center with the old notion of incenter.