Scaling exponents of curvature measures

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286403" target="_blank" >RIV/00216208:11320/14:10286403 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4171/JFG/5" target="_blank" >http://dx.doi.org/10.4171/JFG/5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/JFG/5" target="_blank" >10.4171/JFG/5</a>

Result language
angličtina
Original language name
Scaling exponents of curvature measures
Original language description
Fractal curvatures of a compact set F in Rd are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets of F as diametr tends to 0 and have been studied in the last years in particular for self-similar and self-conformalsets. In the present paper we study the nongeneric situation when the scaling exponents are not determined by the dimension of F . We demonstrate that the possibilities for nongeneric behaviour are rather limited and introduce the notion of local flatness, which allows a geometric characterization of nongenericity in R and R2. We expect local flatness to be characteristic also in higher dimensions. The results enlighten the geometric meaning of the scaling exponents.
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
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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