Flag representations of mixed volumes and mixed functionals of convex bodies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384458" target="_blank" >RIV/00216208:11320/18:10384458 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jmaa.2017.12.039" target="_blank" >https://doi.org/10.1016/j.jmaa.2017.12.039</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.12.039" target="_blank" >10.1016/j.jmaa.2017.12.039</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Flag representations of mixed volumes and mixed functionals of convex bodies

Popis výsledku v původním jazyce

Mixed volumes V(K-1, ... , K-d) of convex bodies K-1, ... , K-d in Euclidean space R-d are of central importance in the Brunn-Minkowski theory. Representations for mixed volumes are available in special cases, for example as integrals over the unit sphere with respect to mixed area measures. More generally, in Hug-Rataj-Weil (2013) [11] a formula for V(K[n], M[d - n]), n is an element of {1, ... , d - 1), as a double integral over flag manifolds was established which involved certain flag measures of the convex bodies K and M (and required a general position of the bodies). In the following, we discuss the general case V(K-1[n(1)], ... , K-k[n(k)]), n(1) + ... + n(k) = d, and show a corresponding result involving the flag measures Omega(n1) (K-1;.), ... , Omega(nk) (K-k;.). For this purpose, we first establish a curvature representation of mixed volumes over the normal bundles of the bodies involved. We also obtain a corresponding flag representation for the mixed functionals from translative integral geometry and a local version, for mixed (translative) curvature measures.

Název v anglickém jazyce

Flag representations of mixed volumes and mixed functionals of convex bodies

Popis výsledku anglicky

Mixed volumes V(K-1, ... , K-d) of convex bodies K-1, ... , K-d in Euclidean space R-d are of central importance in the Brunn-Minkowski theory. Representations for mixed volumes are available in special cases, for example as integrals over the unit sphere with respect to mixed area measures. More generally, in Hug-Rataj-Weil (2013) [11] a formula for V(K[n], M[d - n]), n is an element of {1, ... , d - 1), as a double integral over flag manifolds was established which involved certain flag measures of the convex bodies K and M (and required a general position of the bodies). In the following, we discuss the general case V(K-1[n(1)], ... , K-k[n(k)]), n(1) + ... + n(k) = d, and show a corresponding result involving the flag measures Omega(n1) (K-1;.), ... , Omega(nk) (K-k;.). For this purpose, we first establish a curvature representation of mixed volumes over the normal bundles of the bodies involved. We also obtain a corresponding flag representation for the mixed functionals from translative integral geometry and a local version, for mixed (translative) curvature measures.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA15-08218S" target="_blank" >GA15-08218S: Teorie reálných funkcí a její aplikace v geometrii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

460

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

745-776

Kód UT WoS článku

000425705800017

EID výsledku v databázi Scopus

2-s2.0-85038383908