The paper shows that no origin-symmetric convex polyhedron in R^3 is the intersection body of a star body. It is shown also that every origin-symmetric convex body in R^d, 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.

Campi, S. (1999). Convex intersection bodies in three and four dimensions”. MATHEMATIKA, 46, 15-27.

Convex intersection bodies in three and four dimensions”

CAMPI, STEFANO
1999

Abstract

The paper shows that no origin-symmetric convex polyhedron in R^3 is the intersection body of a star body. It is shown also that every origin-symmetric convex body in R^d, 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/22004
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