Let H be a convex body in Euclidean 3-space. Define γ5(H) to be the supremum of the volume ratio V(P)/V(H) as P ranges over all convex polyhedra in H which have at most 5 vertices. We prove that the minimum of γ5(H) over all convex bodies is attained if and only if H is an ellipsoid.
Poliedri inscritti in insiemi convessi: una proprieta' estremale / Bianchi, Gabriele. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B. - ISSN 0392-4041. - STAMPA. - 5:(1986), pp. 767-780.
Poliedri inscritti in insiemi convessi: una proprieta' estremale
BIANCHI, GABRIELE
1986
Abstract
Let H be a convex body in Euclidean 3-space. Define γ5(H) to be the supremum of the volume ratio V(P)/V(H) as P ranges over all convex polyhedra in H which have at most 5 vertices. We prove that the minimum of γ5(H) over all convex bodies is attained if and only if H is an ellipsoid.
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