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The slices of a cone and a characterization of ellipsoids

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Mathieu Meyer  and
Marc Rogalski
Mathieu Meyer
Affiliation:
Equipe d/Analyse et de Mathématiques appliquées, Université de Marne-la-Vallée, 5, boulevard Descartes, 77454 Marne-la-Vallée, France.
Marc Rogalski
Affiliation:
Equipe d'Analyse, Université Paris 6, 4, place Jussieu, 75242 Paris cedex 05, France.
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Abstracat

Let C be a convex cone in ℛd with non-empty interior and a compact basis K. If H1 and H2 are any two parallel hyperplanes tangent to K, whose slices with C are two other compact basis K1 and K2, let D, D1 and D2 be the truncated subcones of C generated by K, K1 and K2. We prove that K is an ellipsoid if, and only if, vol (D)2 = vol (D1) vol (D2) for every such pair of hyperplanes H1, and H2.

MSC classification

Secondary: 52A38: Length, area, volume
Type
Research Article
Information
Mathematika , Volume 45 , Issue 2 , December 1998 , pp. 305 - 317
Copyright
Copyright © University College London 1998

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References

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