Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-12828
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Main Title: A discrete version of Liouville’s theorem on conformal maps
Author(s): Pinkall, Ulrich
Springborn, Boris
Type: Article
URI: https://depositonce.tu-berlin.de/handle/11303/14055
http://dx.doi.org/10.14279/depositonce-12828
License: https://creativecommons.org/licenses/by/4.0/
Abstract: 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.
Subject(s): conformal flatness
discrete conformal map
Möbius transformation
Issue Date: 15-Apr-2021
Date Available: 15-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: DFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamik
TU Berlin, Open-Access-Mittel – 2021
Journal Title: Geometriae Dedicata
Publisher: Springer Nature
Volume: 214
Issue: 1
Publisher DOI: 10.1007/s10711-021-00621-2
Page Start: 389
Page End: 398
EISSN: 1572-9168
ISSN: 0046-5755
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Differentialgeometrie
Appears in Collections:Technische Universität Berlin » Publications

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