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Beiträge zur Algebra und Geometrie - Contributions to Algebra and Geometry

, Volume 55, Issue 2, pp 595–602

First Online: 06 November 2013Received: 02 September 2013Accepted: 17 October 2013


It is well known that the set of centers of minimal balls containing a convex body is a singleton, but the set of incenters of that body, i.e., its kernel, need not be a singleton. On the other hand, the kernel cannot have the same dimension as the body itself. By iterating the construction of the kernel we define a new selector, the kernel center, which selects a point from the kernel of a given convex body. Evidently, this selector is constant when restricted to the family of parallel bodies of a fixed convex body. We prove that it is directly additive but not additive, and we study further properties of this selector.

KeywordsConvex body Selector Kernel Inradius Minkowski direct additivity Second author is supported by MEC and FEDER project MTM2011-25377 and by -Programa de Ayudas a Grupos de Excelencia de la Región de Murcia-, Fundación Séneca, 04540-GERM-06.

Mathematics Subject Classification 1991Primary 52A20 Secondary 52A99  Download fulltext PDF

Autor: Maria Moszyńska - E. Saorín Gómez

Fuente: https://link.springer.com/

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