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The Szökefalvi-Nagy Problem

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

Abstract

Let M ⊂ R n be a compact, convex body. We consider the family T(M) of all its translates (Fig. 111) and denote by him M the Helly dimension of T(M): him M = him T(M). This chapter is devoted to the Helly-dimensional classification of compact, convex bodies. In other words, we are going to consider the following problem: to give a geometrical description of the compact, convex bodies M ⊂ R n satisfying him M = r, where 1 ≤ r ≤ n. By reasons which will be mentioned in this section, this problem is said to be the Szökefalvi-Nagy problem.

Keywords

Convex Body Vector System Nonzero Vector Direct Decomposition Symmetric Body 
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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