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• W2963625864 abstract "Abstract The k th projection function υ k ( K , ·) of a convex body K ⊂ ℝ d , d ≥ 3, is a function on the Grassmannian G ( d , k ) which measures the k -dimensional volume of the projection of K onto members of G ( d , k ). For k = 1 and k = d − 1, simple formulas for the projection functions exist. In particular, υ d -1 ( K , ·) can be written as a spherical integral with respect to the surface area measure of K . Here, we generalize this result and prove two integral representations for υ k ( K , ·), k = 1,..., d − 1, over flag manifolds. Whereas the first representation generalizes a result of Ambartzumian (1987), but uses a flag measure which is not continuous in K , the second representation is related to a recent flag formula for mixed volumes by Hug, Rataj and Weil (2013) and depends continuously on K ." @default.
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• W2963625864 date "2017-07-01" @default.
• W2963625864 modified "2023-09-23" @default.
• W2963625864 title "A flag representation of projection functions" @default.
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• W2963625864 doi "https://doi.org/10.1515/advgeom-2017-0022" @default.
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