Lipschitz Smoothings of Polyhedral Manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917852866412544 |
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| author | Cattalani, Spencer |
| author_facet | Cattalani, Spencer |
| contents | We use a recent result of C. Lange to obtain a converse to a theorem of B. Bowditch in dimension at most $4$. In particular, we show that, for $n \leq 4$, a polyhedral $n$-manifold $X$ with bounded geometry is $K$-bi-Lipschitz homeomorphic to a Riemannian manifold $M$. We bound the constant $K$, the curvature, and the injectivity radius of $M$ by the bounds on the geometry of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lipschitz Smoothings of Polyhedral Manifolds Cattalani, Spencer Differential Geometry 57R12, 52B70 We use a recent result of C. Lange to obtain a converse to a theorem of B. Bowditch in dimension at most $4$. In particular, we show that, for $n \leq 4$, a polyhedral $n$-manifold $X$ with bounded geometry is $K$-bi-Lipschitz homeomorphic to a Riemannian manifold $M$. We bound the constant $K$, the curvature, and the injectivity radius of $M$ by the bounds on the geometry of $X$. |
| title | Lipschitz Smoothings of Polyhedral Manifolds |
| topic | Differential Geometry 57R12, 52B70 |
| url | https://arxiv.org/abs/2412.00384 |