| Title:
|
Properties of distance functions on convex surfaces and applications (English) |
| Author:
|
Rataj, Jan |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
247-269 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
If $X$ is a convex surface in a Euclidean space, then the squared intrinsic distance function $\mathop {{\rm dist}}^2(x,y)$ is DC (d.c., delta-convex) on $X\times X$ in the only natural extrinsic sense. An analogous result holds for the squared distance function $\mathop {{\rm dist}}^2(x,F)$ from a closed set $F \subset X$. Applications concerning $r$-boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface are given. (English) |
| Keyword:
|
distance function |
| Keyword:
|
convex surface |
| Keyword:
|
Alexandrov space |
| Keyword:
|
DC manifold |
| Keyword:
|
ambiguous locus |
| Keyword:
|
skeleton |
| Keyword:
|
$r$-boundary |
| MSC:
|
52A20 |
| MSC:
|
53C45 |
| idZBL:
|
Zbl 1224.53105 |
| idMR:
|
MR2782772 |
| DOI:
|
10.1007/s10587-011-0010-5 |
| . |
| Date available:
|
2011-05-23T12:46:29Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141531 |
| . |
| Reference:
|
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