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Centers and partial volumes of convex cones II. Advanced topics

  • Alberto  Seeger Email author
  • Mounir Torki
Original Paper

Abstract

This is the second part of an extensive work on volumetric centers and least partial volumes of proper cones in \(\mathbb {R}^n\). The first part [cf. Seeger and Torki (Beiträge Algebra Geom, 2014) Centers and partial volumes of convex cones. I: Basic theory] was devoted to presenting the general theory. We now treat some more specialized issues. The notion of least partial volume is a reasonable alternative to the classical concept of solid angle, whereas the concept of volumetric center is an alternative to the old notion of incenter.

Keywords

Partial volume of a convex cone Solid angle Volumetric center Incenter Homogeneous cone Blaschke-Santaló inequality 

Mathematics Subject Classification

51M25 52A38 47L07 

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Copyright information

© The Managing Editors 2014

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité d’AvignonAvignonFrance
  2. 2.Université d’AvignonCERIAvignonFrance

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