A discrete version of Liouville's theorem on conformal maps

Liouville's theorem says that in dimension greater than two, all conformal maps are M\"obius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally equivalent if they are combinatorially equivalent a...

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Bibliographic Details
Main Authors Pinkall, Ulrich, Springborn, Boris
Format Journal Article
LanguageEnglish
Published 03.11.2019
Subjects
Mathematics - Combinatorics
Mathematics - Complex Variables
Mathematics - Differential Geometry
Mathematics - Geometric Topology
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Summary:Liouville's theorem says that in dimension greater than two, all conformal maps are M\"obius 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.
DOI:10.48550/arxiv.1911.00966