ISSN:
1572-9168
Keywords:
52A40
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider the class of convex bodies in ℝ n with prescribed projection (n − 1)-volumes along finitely many fixed directions. We prove that in such a class there exists a unique body (up to translation) with maximumn-volume. The maximizer is a centrally symmetric polytope and the normal vectors to its facets depend only on the assigned directions. Conditions for the existence of bodies with minimumn-volume in the class defined above are given. Each minimizer is a polytope, and an upper bound for the number of its facets is established.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01264932
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