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- Projection_body abstract "In convex geometry, the projection body ΠK of a centrally symmetric body K in Euclidean space is the star body such that for any vector u, the support function of ΠK in the direction u is the (n – 1)-dimensional volume of the projection of K onto the hyperplane u⊥. The intersection body of K is defined similarly, as the star body such that for any vector u the radial function of IK from the origin in direction u is the (n – 1)-dimensional volume of the intersection of K with the hyperplane u⊥.Projection bodies were discussed by Petty (1967), and intersection bodies were introduced by Lutwak (1988).Minkowski showed that the projection body of a convex body is convex.Koldobsky (1998a) showed that a centrally symmetric star-shaped body is an intersection body if and only if the function 1/||x|| is a positive definite distribution, where ||x|| is the homogeneous function of degree 1 that is 1 on the boundary of the body, and Koldobsky (1998b) used this to show that the unit balls lpn, 1 < p ≤ ∞ in n-dimensional space with the lp norm are intersection bodies for n=4 but are not intersection bodies for n ≥ 5.".
- Projection_body wikiPageExternalLink books?id=UIjyTgEACAAJ.
- Projection_body wikiPageExternalLink aima.1998.1718.
- Projection_body wikiPageExternalLink BFb0081746.
- Projection_body wikiPageExternalLink 0001-8708(88)90077-1.
- Projection_body wikiPageExternalLink 120.4koldobsky.pdf.
- Projection_body wikiPageID "33350956".
- Projection_body wikiPageRevisionID "454817306".
- Projection_body b "n".
- Projection_body hasPhotoCollection Projection_body.
- Projection_body p "p".
- Projection_body subject Category:Convex_geometry.
- Projection_body comment "In convex geometry, the projection body ΠK of a centrally symmetric body K in Euclidean space is the star body such that for any vector u, the support function of ΠK in the direction u is the (n – 1)-dimensional volume of the projection of K onto the hyperplane u⊥.".
- Projection_body label "Projection body".
- Projection_body sameAs m.0h7ny__.
- Projection_body sameAs Q7249443.
- Projection_body sameAs Q7249443.
- Projection_body wasDerivedFrom Projection_body?oldid=454817306.
- Projection_body isPrimaryTopicOf Projection_body.