On reduced spherical bodies
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912022137929728 |
|---|---|
| author | Musielak, Michał |
| author_facet | Musielak, Michał |
| contents | This thesis consists of five papers about reduced spherical convex bodies and in particular spherical bodies of constant width on the $d$-dimensional sphere $S^d$. In paper I we present some facts describing the shape of reduced bodies of thickness under $\fracπ{2}$ on $S^2$. We also consider reduced bodies of thickness at least $\fracπ{2}$, which appear to be of constant width. Paper II focuses on bodies of constant width on $S^d$. We present the properties of these bodies and in particular we discuss conections between notions of constant width and of constant diameter. In paper III we estimate the diameter of a reduced convex body. The main theme of paper IV is estimating the radius of the smallest disk that covers a reduced convex body on $S^2$. The result of paper V is showing that every spherical reduced polygon $V$ is contained in a disk of radius equal to the thickness of this body centered at a boundary point of $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07036 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On reduced spherical bodies Musielak, Michał Metric Geometry This thesis consists of five papers about reduced spherical convex bodies and in particular spherical bodies of constant width on the $d$-dimensional sphere $S^d$. In paper I we present some facts describing the shape of reduced bodies of thickness under $\fracπ{2}$ on $S^2$. We also consider reduced bodies of thickness at least $\fracπ{2}$, which appear to be of constant width. Paper II focuses on bodies of constant width on $S^d$. We present the properties of these bodies and in particular we discuss conections between notions of constant width and of constant diameter. In paper III we estimate the diameter of a reduced convex body. The main theme of paper IV is estimating the radius of the smallest disk that covers a reduced convex body on $S^2$. The result of paper V is showing that every spherical reduced polygon $V$ is contained in a disk of radius equal to the thickness of this body centered at a boundary point of $V$. |
| title | On reduced spherical bodies |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2409.07036 |