\(k\)-codimensional projection bodies
type: Item
instance of: scholarly article
title: \(k\)-codimensional projection bodies
zbMATH Open document ID: 1505.52009
author: Youjiang Lin
author: Yuchi Wu
published in: Advances in Applied Mathematics
publication date: 2022-09-30T00:00:00Z
review text: Motivated by the definition of the well-known projection body (see [\textit{C. M. Petty}, Proc. Colloq. Convexity, Copenhagen 1965, 234--241 (1967; Zbl 0152.20601); \textit{T. Wang}, Adv. Math. 230, No. 4--6, 2457--2473 (2012; Zbl 1257.46016)]), the authors introduce \(k\)-codimensional projection bodies for sets of finite permiter. This is a convex body in \(\mathbb{R}^{n-k+1}\), and it depends on the choice of the coordinate system. The case \(k=1\) corresponds to the classical \(n\)-dimensional projection body only for special sets. In analogy to the classical setting, the authors prove \(k\)-codimensional projection inequalities.
reviewed by: Martin Henk
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 7595591
zbMATH Keywords: projection body
zbMATH Keywords: function of bounded variation
zbMATH Keywords: set of finite perimeter
zbMATH Keywords: Steiner symmetrization
MaRDI profile type: Publication
full work available at URL: j.aam.2022.102435
OpenAlex ID: W4296491873
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DOI: 10.1016/J.AAM.2022.102435
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