A characterization of dual quermassintegrals and the roots of dual Steiner polynomials

DOI10.1016/j.aim.2018.04.008zbMath1393.52005arXiv1707.01675OpenAlexW2963260539WikidataQ129579063 ScholiaQ129579063MaRDI QIDQ1647392

Martin Henk, David Alonso-Gutiérrez, María A. Hernández Cifre

Publication date: 26 June 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.01675

zbMATH Keywords

moment problemdual quermassintegralslocation of rootsShephard's problemdual Steiner polynomials

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Mixed volumes and related topics in convex geometry (52A39) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items

On the roots of polynomials with log-convex coefficients, Random inscribed polytopes in projective geometries, Starshaped sets, Asymptotic normality for random polytopes in non-Euclidean geometries, On the (Dual) Blaschke diagram

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Operations between sets in geometry
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Cyclic convex bodies and optimization moment problems
• A positive solution to the Busemann-Petty problem in \(\mathbb{R}^4\)
• An analytic solution to the Busemann-Petty problem on sections of convex bodies
• Subspace concentration of dual curvature measures of symmetric convex bodies
• Necessary subspace concentration conditions for the even dual Minkowski problem
• A positive answer to the Busemann-Petty problem in three dimensions
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Star valuations and dual mixed volumes
• Dual mixed volumes
• The isoperimetrix in the dual Brunn-Minkowski theory
• The dual Brunn-Minkowski theory for bounded Borel sets: dual affine quermassintegrals and inequalities
• The Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities
• Characterizing the dual mixed volume via additive functionals
• Inequalities between mixed volumes of convex sets
• STEINER POLYNOMIALS VIA ULTRA-LOGCONCAVE SEQUENCES
• The Moment Problem
• Convex Bodies The Brunn-MinkowskiTheory
• A Generalization of a Theorem of Bôcher
• $p$-Means of Convex Bodies.