Flag representations of mixed volumes and mixed functionals of convex bodies

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Flag representations of mixed volumes and mixed functionals of convex bodies
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-08218S" target="_blank" >GA15-08218S: Theory of real functions and its applications in geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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