Mixed curvature measures of translative integral geometry
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384531" target="_blank" >RIV/00216208:11320/18:10384531 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10711-017-0278-1" target="_blank" >https://doi.org/10.1007/s10711-017-0278-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10711-017-0278-1" target="_blank" >10.1007/s10711-017-0278-1</a>
Alternative languages
Result language
angličtina
Original language name
Mixed curvature measures of translative integral geometry
Original language description
The curvature measures of a set X with singularities are measures concentrated on the normal bundle of X, which describe the local geometry of the set X. For given finitely many convex bodies or, more generally, sets with positive reach, the translative integral formula for curvature measures relates the integral mean of the curvature measures of the intersections of the given sets, one fixed and the others translated, to the mixed curvature measures of the given sets. In the case of two sets of positive reach, a representation of these mixed measures in terms of generalized curvatures, defined on the normal bundles of the sets, is known. For more than two sets, a description of mixed curvature measures in terms of rectifiable currents has been derived previously. Here we provide a representation of mixed curvature measures of sets with positive reach based on generalized curvatures. The special case of convex polyhedra is treated in detail.
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/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)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Geometriae Dedicata
ISSN
0046-5755
e-ISSN
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Volume of the periodical
195
Issue of the periodical within the volume
1
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
20
Pages from-to
101-120
UT code for WoS article
000437122700006
EID of the result in the Scopus database
2-s2.0-85027718482