Translative integral formulae for convex bodies (Q1096181)
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scientific article; zbMATH DE number 4030365
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Translative integral formulae for convex bodies |
scientific article; zbMATH DE number 4030365 |
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Translative integral formulae for convex bodies (English)
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1987
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Suppose K is a convex body in d-space, \(\bar K\) a d-dimensional right cylinder based on a convex body K' in a \((d-q) - \)dimensional subspace L. This paper studies the integral over all translations x in L of the intrinsic volume of \(K\cap (\bar K+x);\) the integration is with respect to Lebesgue measure, suitably normalized. The authors describe the integral as a sum of expressions involving mixed volumes of K, K' and the unit ball in q-space. The cases in which K, K' have central symmetry is treated in more detail.
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translation integral
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quermassintegrals of convex bodies
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mixed volumes
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central symmetry
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