On the structure of WDC sets

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the structure of WDC sets

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the structure of WDC sets

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA15-08218S" target="_blank" >GA15-08218S: Teorie reálných funkcí a její aplikace v geometrii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematische Nachrichten

ISSN

0025-584X

e-ISSN

—

Svazek periodika

292

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

32

Strana od-do

1595-1626

Kód UT WoS článku

000479005500009

EID výsledku v databázi Scopus

2-s2.0-85063639887