Centers and partial volumes of convex cones. Part II: Advanced topics.

Alberto Seeger (1) , Mounir Torki (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 LIA - Laboratoire Informatique d'Avignon

This is the second part of an extensive work on volumetric centers and least partial volumes of proper cones in 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.

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

Domaines: Mathématiques [math]

Alberto Seeger, Mounir Torki. Centers and partial volumes of convex cones. Part II: Advanced topics.. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2015, 56 (2), pp.491-514. ⟨10.1007/s13366-014-0221-7⟩. ⟨hal-01326181⟩