منابع مشابه
Convex-Bodies with Similar Projections
By examining an example constructed by Petty and McKinney, we show that there are pairs of centered and coaxial bodies of revolution in Ed, d > 3, whose projections onto each two-dimensional subspace are similar, but which are not themselves even affinely equivalent.
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In [F] Firey extended the notion of the Minkowski sum, and introduced, for each real p, a new linear combination of convex bodies, that he called p-sums. Lutwak [Lu2], [Lu3] showed that these Firey sums lead to a Brunn-Minkowski theory for each p ≥ 1. He introduced the notions of p-mixed volume, p-surface area measure, and proved an integral representation and inequalities for p-mixed volumes, ...
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We prove that for every M-dimensional body K, there is a rectangular parallelepiped B of the same volume as K, such that the projection of B onto any coordinate subspace is at most as large as that of the corresponding projection of K. We apply this theorem to projections of finite set systems and to hereditary properties. In particular, we show that every hereditary property of uniform hypergr...
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Abstract. The Fourier analytic approach to sections of convex bodies has recently been developed and has led to several results, including a complete analytic solution to the BusemannPetty problem, characterizations of intersection bodies, extremal sections of lp-balls. In this article, we extend this approach to projections of convex bodies and show that the projection counterparts of the resu...
متن کاملThe concept of duality for measure projections of convex bodies ✩
We show that an involution T on some class of functions on Rn, which reverses order (meaning that if f g then T f T g) has, often, a very specific form, actually essentially unique. It is done in this paper for the class of s-concave functions, for which this unique formula is derived. These functions are, for integer s, exactly marginals of convex bodies of dimension n+ s. This understanding i...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01760-1