Uniform boundedness on extremal subsets in Alexandrov spaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916540295675904 |
|---|---|
| author | Fujioka, Tadashi |
| author_facet | Fujioka, Tadashi |
| contents | In this paper, we study extremal subsets in Alexandrov spaces with dimension $n$, curvature $\geκ$, and diameter $\le D$. We show that the following three quantities are uniformly bounded above in terms of $n$, $κ$, and $D$: (1) the number of extremal subsets in an Alexandrov space; (2) the Betti numbers of an extremal subset; (3) the volume of an extremal subset. The proof is an application of essential coverings introduced by Yamaguchi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_00603 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Uniform boundedness on extremal subsets in Alexandrov spaces Fujioka, Tadashi Differential Geometry Metric Geometry 53C20, 53C23 In this paper, we study extremal subsets in Alexandrov spaces with dimension $n$, curvature $\geκ$, and diameter $\le D$. We show that the following three quantities are uniformly bounded above in terms of $n$, $κ$, and $D$: (1) the number of extremal subsets in an Alexandrov space; (2) the Betti numbers of an extremal subset; (3) the volume of an extremal subset. The proof is an application of essential coverings introduced by Yamaguchi. |
| title | Uniform boundedness on extremal subsets in Alexandrov spaces |
| topic | Differential Geometry Metric Geometry 53C20, 53C23 |
| url | https://arxiv.org/abs/1809.00603 |