Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 551-563 (1999)

Fixing and Hindering Systems in Combinatorial Geometry

V. Boltyanski, H. Martini

Technische Universität Chemnitz, Mathematische Fakultät, 09107 Chemnitz, Germany

Abstract: In the first and in the second section of the article we give a short survey of former results and new observations on fixing and hindering systems for compact, convex bodies. In the third part, we prove some results on fixing and hindering systems for $d$-convex bodies in Minkowski spaces. In particular, finite-dimensional normed spaces are considered, for which the unit ball is the polar body of a belt body (or, particularly, of a zonoid).

Keywords: convex body, primitive fixing system, primitive hindering system, Minkowski space, equatorial subspace, belt vector, belt body, zonoid.

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