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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
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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

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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