On the structure of WDC sets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10403232" target="_blank" >RIV/00216208:11320/19:10403232 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=NXsr6f3NpE" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=NXsr6f3NpE</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201700253" target="_blank" >10.1002/mana.201700253</a>
Alternative languages
Result language
angličtina
Original language name
On the structure of WDC sets
Original language description
WDC sets in Rd were recently defined as sublevel sets of DC functions (differences of convex functions) at weakly regular values. They form a natural and substantial generalization of sets with positive reach and still admit the definition of curvature measures. Using results on singularities of convex functions, we obtain regularity results on the boundaries of WDC sets. In particular, the boundary of a compact WDC set can be covered by finitely many DC surfaces. More generally, we prove that any compact WDC set M of topological dimension k <= d can be decomposed into the union of two sets, one of them being a k-dimensional DC manifold open in M, and the other can be covered by finitely many DC surfaces of dimension k-1. We also characterize locally WDC sets among closed Lipschitz domains and among lower-dimensional Lipschitz manifolds. Finally, we find a full characterization of locally WDC sets in theplane.
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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematische Nachrichten
ISSN
0025-584X
e-ISSN
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Volume of the periodical
292
Issue of the periodical within the volume
7
Country of publishing house
DE - GERMANY
Number of pages
32
Pages from-to
1595-1626
UT code for WoS article
000479005500009
EID of the result in the Scopus database
2-s2.0-85063639887