Characterization of Minkowski measurability in terms of surface area

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10140149" target="_blank" >RIV/00216208:11320/13:10140149 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.10.059" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2012.10.059</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.10.059" target="_blank" >10.1016/j.jmaa.2012.10.059</a>

Result language
angličtina
Original language name
Characterization of Minkowski measurability in terms of surface area
Original language description
The r-parallel set to a set A in Euclidean space consists of all points with distance at most r from A. Recently, the asymptotic behaviour of volume and surface area of the parallel sets as r tends to 0 has been studied and some general results regardingtheir relations have been established. Here we complete the picture regarding the resulting notions of Minkowski content and S-content. In particular, we show that a set is Minkowski measurable if and only if it is S-measurable, i.e. if and only if itsS-content is positive and finite, and that positivity and finiteness of the lower and upper Minkowski contents imply the same for the S-contents and vice versa. The results are formulated in the more general setting of Kneser functions. Furthermore, therelations between Minkowski and S-contents are studied for more general gauge functions. The results are applied to simplify the proof of the Modified Weyl-Berry conjecture in dimension one.
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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