On the dimension of k-medial axis for arbitrary closed set
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911847724089344 |
|---|---|
| author | Liang, Xiangyu |
| author_facet | Liang, Xiangyu |
| contents | We prove that the k-medial axis of an arbitrary closed set in Rn is n-k+1-rectifiable (and hence of dimension at most n-k+1). This result gives a first stratification for medial axis of any closed set, which has been widely studied and used in pure and applied mathematics. This also answers a question proposed by Erdos[4], and leads to more further interesting investigations (see the end of the article). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the dimension of k-medial axis for arbitrary closed set Liang, Xiangyu Classical Analysis and ODEs 28A75, 52A38 We prove that the k-medial axis of an arbitrary closed set in Rn is n-k+1-rectifiable (and hence of dimension at most n-k+1). This result gives a first stratification for medial axis of any closed set, which has been widely studied and used in pure and applied mathematics. This also answers a question proposed by Erdos[4], and leads to more further interesting investigations (see the end of the article). |
| title | On the dimension of k-medial axis for arbitrary closed set |
| topic | Classical Analysis and ODEs 28A75, 52A38 |
| url | https://arxiv.org/abs/2404.13540 |