Width-integrals of convex bodies
نویسندگان
چکیده
منابع مشابه
Width-integrals and Affine Surface Area of Convex Bodies
The main purposes of this paper are to establish some new Brunn– Minkowski inequalities for width-integrals of mixed projection bodies and affine surface area of mixed bodies, together with their inverse forms.
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is isotropic with respect to an appropriate measure depending on f . The purpose of this note is to provide applications of this point of view in the case of the mean width functional T 7→ w(TK) under various constraints. Recall that the width of K in the direction of u ∈ Sn−1 is defined by w(K,u) = hK(u) + hK(−u), where hK(y) = maxx∈K〈x, y〉 is the support function of K. The width function w(K,...
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For a convex body K ⊂ Rn, the kth projection function of K assigns to any k-dimensional linear subspace of Rn the k-volume of the orthogonal projection of K to that subspace. Let K and K0 be convex bodies in Rn, and let K0 be centrally symmetric and satisfy a weak regularity and curvature condition (which includes all K0 with ∂K0 of class C2 with positive radii of curvature). Assume that K and ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0383254-5