\(L_p\)-dual affine surface area
type: Item
instance of: scholarly article
title: \(L_p\)-dual affine surface area
zbMATH Open document ID: 1158.52005
author: Wei Wang
author: Binwu He
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-10-22T00:00:00Z
review text: A definition of affine surface area \(\Omega(K)\) of a convex body \(K\) in \(\mathbb{R}^n\) by \textit{K. Leichtweiß} [Manuscr. Math. 65, No.~2, 181--197 (1989; Zbl 0685.53012)] was generalized by \textit{E. Lutwak} [Adv. Math. 118, No.~2, 244--294 (1996; Zbl 0853.52005)] to \(L_p\)-affine surface area \(\Omega_p(K)\) by using Brunn-Minkowski-Fiery theory. In the present paper, the authors introduce \(L_p\)-dual affine surface area using \(L_p\)-dual mixed volumes defined by E. Lutwak [loc. cit.]. With respect to this area functional inequalities are presented (affine isoperimetric, Blaschke-Santaló, Brunn-Minkowski).
reviewed by: Friedrich Manhart
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 52A39
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 5355971
zbMATH Keywords: \(L_p\)-dual surface area
zbMATH Keywords: \(L_p\)-dual mixed volume
zbMATH Keywords: Blaschke-Santaló inequality
zbMATH Keywords: affine isoperimetric inequality
zbMATH Keywords: Brunn-Minkowski inequality
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.08.006
OpenAlex ID: W2021603418
cites work: Zonoids with Minimal Volume-Product--A New Proof
cites work: Zur Affinoberfläche konvexer Körper. (On affine surfaces of convex bodies)
cites work: Über einige Eigenschaften der Affinoberfläche beliebiger konvexer Körper. (On some properties of the affine surface area of arbitrary convex bodies)
cites work: Bemerkungen zur Definition einer erweiterten Affinoberfläche von E. Lutwak. (Remarks on the definition of extended affine surface area given by E. Lutwak)
cites work: On the history of the affine surface area for convex bodies
cites work: Q4377597
cites work: Q4778514
cites work: A characterization of affine surface area
cites work: \(\mathrm{SL}(n)\) invariant valuations on polytopes
cites work: Q3697820
cites work: On some affine isoperimetric inequalities
cites work: Mixed affine surface area
cites work: Extended affine surface area
cites work: The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
cites work: On the \(p\)-affine surface area
cites work: Geominimal surface area
cites work: Zonoids with minimal volume-product
cites work: Q5287551
cites work: On the Affine Surface Area
cites work: Surface bodies and \(p\)-affine surface area
cites work: \(L_{p}\)-mixed affine surface area
cites work: Illumination bodies and affine surface area
cites work: New \(L_p\) affine isoperimetric inequalities
cites work: Q3593803
DOI: 10.1016/J.JMAA.2008.08.006
description: scientific article; zbMATH DE number 5355971