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Convex intersection bodies in three and four dimensions

Part of:General convexity

Published online by Cambridge University Press:  26 February 2010

Stefano Campi
Stefano Campi
Affiliation:
Departimento di Matematica Pura e Applicata “G. Vitali”, Università degli Studi di Modena, Via Campi 213/B, 41100 Modena. Italy.
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Abstract

The paper shows that no origin-symmetric convex polyhedron in R3 is the intersection body of a star body. It is shown also that every originsymmetric convex body in Rd, for d = 3 and 4, can be seen as the intersection body of a star-shaped set whose radial function satisfies conditions related to suitable non-integer Sobolev classes.

MSC classification

Secondary:52A30: Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)

Information

Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999, pp. 15 - 27
Copyright
Copyright © University College London 1999

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