Geodesic
A representation for the support function of a convex body
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2015), pp. 3-7

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In this paper a formula for a translation invariant measure of planes intersecting a $n$-dimensional convex body in terms of curvatures of $2$-dimensional projections of the body was found. The paper also gives a new simple proof of the representation for the support function of an origin symmetric $3$-dimensional convex body, which was obtained by means of a stochastic approximation of the convex body.
Keywords: integral geometry, convex body, zonoid, support function. 
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R. H. Aramyan; A. G. Manucharyan. A representation for the support function of a convex body. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2015), pp. 3-7. http://geodesic.mathdoc.fr/item/UZERU_2015_3_a0/