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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 &lt;= 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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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