Combinatorial geometry of belt bodies

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


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].


Convex Body Vector System Convergent Sequence Nonzero Vector Supporting Line 
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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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