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Combinatorial geometry of belt bodies

  • Vladimir Boltyanski
  • Horst Martini
  • Petru S. Soltan
Part of the Universitext book series (UTX)

Abstract

In this chapter we consider a new class of convex bodies which was introduced in [Bt 14] and [B-B 2]. This is the class of belt bodies which is much larger than the class of zonoids. (For zonoids and their fascinating properties, the reader is referred to the surveys [S-W], [G-W], [Bk 1], and [Mar 4].) Moreover, the class of belt bodies is dense in the family of all compact, convex bodies. Nevertheless, solutions of combinatorial problems for zonoids [Ba 1, Ba 2, Mar 2, B-SP 5, B-SP 6] can be extended to belt bodies. The aim of this chapter is the explanation of combinatorial properties of belt bodies, cf. also [B-M 1].

Keywords

Convex Body Vector System Convergent Sequence Nonzero Vector Supporting Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vladimir Boltyanski
    • 1
  • Horst Martini
    • 2
  • Petru S. Soltan
    • 3
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.Faculty of MathematicsTU Chemnitz-ZwickauChemnitzGermany
  3. 3.Faculty of MathematicsMoldavian State UniversityKishinevMoldova

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