On volume and surface area of parallel sets. II. Surface measures and (non)differentiability of the volume

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10507643" target="_blank" >RIV/00216208:11320/25:10507643 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vljJ9srC5Q" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vljJ9srC5Q</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.70006" target="_blank" >10.1112/blms.70006</a>

Result language
angličtina
Original language name
On volume and surface area of parallel sets. II. Surface measures and (non)differentiability of the volume
Original language description
We prove that at differentiability points r(0)>0 of the volume function of a compact set A subset of R-d (associating to r the volume of the r-parallel set of A), the surface area measures of r-parallel sets of A converge weakly to the surface area measure of the r(0)-parallel set as r -> r(0). We further study the question which sets of parallel radii can occur as sets of nondifferentiability points of the volume function of some compact set. We provide a full characterization for dimensions d=1 and 2.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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