A flag representation of projection functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369107" target="_blank" >RIV/00216208:11320/17:10369107 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyter.com/view/j/advgeom.2017.17.issue-3/advgeom-2017-0022/advgeom-2017-0022.xml" target="_blank" >https://www.degruyter.com/view/j/advgeom.2017.17.issue-3/advgeom-2017-0022/advgeom-2017-0022.xml</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/advgeom-2017-0022" target="_blank" >10.1515/advgeom-2017-0022</a>
Alternative languages
Result language
angličtina
Original language name
A flag representation of projection functions
Original language description
The kth projection function v(k)(K,.) of a convex body K subset of R-d, d >= 3, is a function on the Grassmannian G(d,k) which measures the k-dimensional volume of the projection of K onto members of G(d,k). For k=1 and k=d-1, simple formulas for the projection functions exist. In particular, v(d-1)(K,.) can be written as a spherical integral with respect to the surface area measure of K. Here, we generalize this result and prove two integral representations for v(k)(K,.), k=1,...,d-1, over flag manifolds. Whereas the first representation generalizes a result of Ambartzumian (1987), but uses a flag measure which is not continuous in K, the second representation is related to a recent flag formula for mixed volumes by Hug, Rataj and Weil (2013) and depends continuously on K.
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/GAP201%2F10%2F0472" target="_blank" >GAP201/10/0472: Stochastic geometry - inhomogeneity, marking, dynamics and stereology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Geometry
ISSN
1615-715X
e-ISSN
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Volume of the periodical
17
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
20
Pages from-to
303-322
UT code for WoS article
000406068000004
EID of the result in the Scopus database
2-s2.0-85026367210