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

Alonso-Gutiérrez, D. (Universidad de Zaragoza) ; Henk, M. ; Hernández Cifre, M.A.

Resumen: Let m=1, (r0=0, r1, …, rm) be a tuple of distinct real numbers and n=2. We provide a characterization of those tuples (¿0, ¿1, …, ¿m) of real numbers such that there exist n-dimensional star bodies K, L with W˜rj(K, L)=¿j, j=0, …, m, where W˜r(K, L) denotes the r-th dual (relative) quermassintegral of K and L. This may be regarded as an analogue within the dual Brunn–Minkowski theory of Shephard''s classification of quermassintegrals of two convex bodies. It turns out that the characterization of dual quermassintegrals is related to the moment problem, and based on this relation, we also derive new determinantal inequalities among the dual quermassintegrals. Moreover, this characterization will be the key tool in order to investigate structural properties of the set of roots of dual Steiner polynomials of star bodies.

Idioma: Inglés

DOI: 10.1016/j.aim.2018.04.008

Año: 2018

Publicado en: Advances in Mathematics 331 (2018), 565-588
ISSN: 0001-8708

Originalmente disponible en: Texto completo de la revista

Factor impacto JCR: 1.435 (2018)

Categ. JCR: MATHEMATICS rank: 43 / 313 = 0.137 (2018) - Q1 - T1

Factor impacto SCIMAGO: 2.514 - Mathematics (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65430-P
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)