Smooth Approximations of Quasispheres
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913784254169088 |
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| author | Cattalani, Spencer |
| author_facet | Cattalani, Spencer |
| contents | We prove that every quasisphere is the Gromov-Hausdorff limit of a sequence of locally smooth uniform quasispheres. We also prove an analogous result in the bi-Lipschitz setting. This extends recent results of D. Ntalampekos from dimension 2 to arbitrary dimension. In the process, we replace the second half of his argument by a completely different, more efficient approach, which should be applicable to other problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09253 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smooth Approximations of Quasispheres Cattalani, Spencer Metric Geometry Complex Variables 30L10, 53C23 We prove that every quasisphere is the Gromov-Hausdorff limit of a sequence of locally smooth uniform quasispheres. We also prove an analogous result in the bi-Lipschitz setting. This extends recent results of D. Ntalampekos from dimension 2 to arbitrary dimension. In the process, we replace the second half of his argument by a completely different, more efficient approach, which should be applicable to other problems. |
| title | Smooth Approximations of Quasispheres |
| topic | Metric Geometry Complex Variables 30L10, 53C23 |
| url | https://arxiv.org/abs/2503.09253 |