A REPRESENTATION FOR THE SUPPORT FUNCTION OF A CONVEX BODY

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Submitted: 2025-02-11; Published: 2025-02-11

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Abstract

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.