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
1999-01-01
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.File in questo prodotto:
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https://hdl.handle.net/11365/22004
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