A discrete version of Liouville's theorem on conformal maps
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866912176831201280 |
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| author | Pinkall, Ulrich Springborn, Boris |
| author_facet | Pinkall, Ulrich Springborn, Boris |
| contents | Liouville's theorem says that in dimension greater than two, all conformal maps are Möbius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally equivalent if they are combinatorially equivalent and the lengths of corresponding edges are related by scale factors associated with the vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_00966 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A discrete version of Liouville's theorem on conformal maps Pinkall, Ulrich Springborn, Boris Differential Geometry Combinatorics Complex Variables Geometric Topology 53A30, 52C26 Liouville's theorem says that in dimension greater than two, all conformal maps are Möbius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally equivalent if they are combinatorially equivalent and the lengths of corresponding edges are related by scale factors associated with the vertices. |
| title | A discrete version of Liouville's theorem on conformal maps |
| topic | Differential Geometry Combinatorics Complex Variables Geometric Topology 53A30, 52C26 |
| url | https://arxiv.org/abs/1911.00966 |