On the (Dual) Blaschke diagram
type: Item
instance of: scholarly article
title: On the (Dual) Blaschke diagram
zbMATH Open document ID: 1473.52003
author: Maria A. Hernández Cifre
author: Miriam Tárraga
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2021-07-15T00:00:00Z
review text: The relation between properties of the roots of Steiner polynomials and the Blaschke diagram is investigated. The behavior of the roots of the Steiner polynomial of a~convex body embedded in a higher dimensional space is studied. In the 3-dimensional case, the involved sets follow a precise pattern when they are mapped into the Blaschke diagram. The so-called dual Blaschke diagram is constructed and characterized. As an immediate consequence, a new characterization of dual quermassintegrals in dimension \(n = 3\) is put forward. The corresponding Blaschke problem in the setting of the so-called dual Brunn-Minkowski theory is studied.
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 52A30
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 7371772
zbMATH Keywords: roots of Steiner polynomials
zbMATH Keywords: dual quermassintegrals
zbMATH Keywords: Blaschke diagram
zbMATH Keywords: dual Blaschke diagram
reviewed by: A. R. Alimov
MaRDI profile type: Publication
full work available at URL: s00574-020-00204-x
OpenAlex ID: W3011582590
cites work: A characterization of dual quermassintegrals and the roots of dual Steiner polynomials
cites work: Q5847704
cites work: STEINER POLYNOMIALS VIA ULTRA-LOGCONCAVE SEQUENCES
cites work: On the roots of the Steiner polynomial of a 3-dimensional convex body
cites work: Refinements of the Brunn-Minkowski inequality
cites work: Dual mixed volumes
cites work: Q4102090
cites work: The Missing Boundary of the Blaschke Diagram
cites work: Convex Bodies The Brunn-MinkowskiTheory
DOI: 10.1007/S00574-020-00204-X
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description: scientific article; zbMATH DE number 7371772