Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T15:37:51.183Z Has data issue: false hasContentIssue false
  • English
  • Français

How do convex bodies sit?

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Tudor Zamfirescu
Tudor Zamfirescu
Affiliation:
Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany
Get access

Extract

Every homogeneous convex body in ℝd (d≥2) put to sit on a horizontal hyperplane finds a position of stable equilibrium. A cube has 2d such positions and an ellipsoid with pairwise distinct axis-lengths has 2. How many positions of stable equilibrium have most convex bodies?

The term “most” is understood in the Baire category sense. For various other results on most convex bodies, see [2], [4].

MSC classification

Secondary: 52A27: Approximation by convex sets
Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995 , pp. 178 - 181
Copyright
Copyright © University College London 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bárány, I. and Zamfirescu, T.. Diameters in typical convex bodies. Can. J. Math., 42 (1990), 50–61.CrossRefGoogle Scholar
2.Gruber, P. M.. Baire categories in Convexity. In: Handbook of Convex Geometry, Editors Gruber, P. and Wills, J. (Elsevier Science, 1993).Google Scholar
3.Zamfirescu, T.. Points on infinitely many normals to convex surfaces. J. Reine Angew. Math., 350 (1984), 183–187.Google Scholar
4.Zamfirescu, T.. Baire categories in Convexity. Atti Sem. Mat. Fis. Univ. Modena, 39 (1991), 139–164.Google Scholar