Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-19T05:31:08.071Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

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

B.Bagby, R. J.. Volumes of cones. American Mathematical Monthly, 103 (1996), 794–796.CrossRefGoogle Scholar
M-W.Meyer, M. and Werner, E.. The Santaló regions of a convex body. Trans. Amer. Math. Soc. (1998) (to appear).Google Scholar
S.Schneider, R.. Convex bodies: The Brunn–Minkowski Theory. Encyclopedia of Math. and its Applic., 44 (Cambridge University Press, 1993).CrossRefGoogle Scholar