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

TL;DR

This paper characterizes dual quermassintegrals of star bodies, relates the problem to the moment problem, derives new inequalities, and explores the roots of dual Steiner polynomials.

Contribution

It provides a new characterization of dual quermassintegrals and investigates the roots of dual Steiner polynomials, linking these to the moment problem.

Findings

Characterization of dual quermassintegrals for star bodies.

New inequalities for dual quermassintegrals.

Structural properties of roots of dual Steiner polynomials.

Abstract

For any $I\subset\mathbb{R}$ finite with $0\in I$, we provide a characterization of those tuples $(\omega_i)_{i\in I}$ of positive numbers which are dual querma\ss integrals of two star bodies. It turns out that this problem is related to the moment problem. Based on this relation we also get new inequalities for the dual querma\ss integrals. Moreover, the above characterization will be the key tool in order to investigate structural properties of the set of roots of dual Steiner polynomials of star bodies.