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Convex intersection bodies in three and four dimensions

Published online by Cambridge University Press:  26 February 2010

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.

Type
Research Article
Copyright
Copyright © University College London 1999

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