Variance of the distance to the boundary of convex domains in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916327746174976 |
|---|---|
| author | Fletcher, Alastair N. Fletcher, Alexander G. |
| author_facet | Fletcher, Alastair N. Fletcher, Alexander G. |
| contents | In this paper, we give for the first time a systematic study of the variance of the distance to the boundary for arbitrary bounded convex domains in $\mathbb{R}^2$ and $\mathbb{R}^3$. In dimension two, we show that this function is strictly convex, which leads to a new notion of the centre of such a domain, called the variocentre. In dimension three, we investigate the relationship between the variance and the distance to the boundary, which mathematically justifies claims made for a recently developed algorithm for classifying interior and exterior points with applications in biology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variance of the distance to the boundary of convex domains in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ Fletcher, Alastair N. Fletcher, Alexander G. General Mathematics 52A10, 52A15, 52A20 In this paper, we give for the first time a systematic study of the variance of the distance to the boundary for arbitrary bounded convex domains in $\mathbb{R}^2$ and $\mathbb{R}^3$. In dimension two, we show that this function is strictly convex, which leads to a new notion of the centre of such a domain, called the variocentre. In dimension three, we investigate the relationship between the variance and the distance to the boundary, which mathematically justifies claims made for a recently developed algorithm for classifying interior and exterior points with applications in biology. |
| title | Variance of the distance to the boundary of convex domains in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ |
| topic | General Mathematics 52A10, 52A15, 52A20 |
| url | https://arxiv.org/abs/2407.12041 |