Normal cycles and curvature measures of sets with d.c. boundary

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10144273" target="_blank" >RIV/00216208:11320/13:10144273 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aim.2013.08.022" target="_blank" >http://dx.doi.org/10.1016/j.aim.2013.08.022</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2013.08.022" target="_blank" >10.1016/j.aim.2013.08.022</a>

Result language
angličtina
Original language name
Normal cycles and curvature measures of sets with d.c. boundary
Original language description
We show that for every compact domain in a Euclidean space with d.c. (delta-convex) boundary there exists a unique Legendrian cycle such that the associated curvature measures fulfill a local version of the Gauss-Bonnet formula. This was known in dimensions two and three and was open in higher dimensions. In fact, we show this property for a larger class of sets including also lower-dimensional sets. We also describe the local index function of the Legendrian cycles and we show that the associated curvature measures fulfill the Crofton formula. (C) 2013 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GCP201%2F10%2FJ039" target="_blank" >GCP201/10/J039: Curvature measures and integral geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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