| Title:
|
A characterization of sets in ${\mathbb R}^2$ with DC distance function (English) |
| Author:
|
Pokorný, Dušan |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
1-38 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a complete characterization of closed sets $F \subset {\mathbb R}^2$ whose distance function $d_F:= {\rm dist}(\cdot ,F)$ is DC (i.e., is the difference of two convex functions on ${\mathbb R}^2$). Using this characterization, a number of properties of such sets is proved. (English) |
| Keyword:
|
distance function |
| Keyword:
|
DC function |
| Keyword:
|
subset of ${\mathbb R}^2$ |
| MSC:
|
26B25 |
| idZBL:
|
Zbl 07511551 |
| idMR:
|
MR4389104 |
| DOI:
|
10.21136/CMJ.2021.0228-20 |
| . |
| Date available:
|
2022-03-25T08:24:57Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149569 |
| . |
| Reference:
|
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