Centers and partial volumes of convex cones. Part I: Basic theory

Abstract : 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.
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Alberto Seeger, Mounir Torki. Centers and partial volumes of convex cones. Part I: Basic theory. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Springer Verlag, 2015, 56 (1), pp.227-248. ⟨10.1007/s13366-014-0220-8⟩. ⟨hal-01326106⟩

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