Convex bodies with extremal volumes having prescribed brightness in finitely many directions |
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Authors: | Stefano Campi Andrea Colesanti Paolo Gronchi |
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Institution: | (1) Dipartimento di Matematica, U. Dini, Viale Morgagni 67/A, 50134 Firenze, Italy |
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Abstract: | We consider the class of convex bodies in
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.Work partially supported by Istituto di Analisi Globale e Applicazioni, CNR, Firenze. |
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Keywords: | 52A40 |
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