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Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller

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Papadopoulos,  Athanase
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Papadopoulos, A. (2018). Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller. In L. Ji (Ed.), Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds & Picard-Fuchs equations (pp. 237-314). Somerville, MA: International Press.


Cite as: https://hdl.handle.net/21.11116/0000-0003-CC57-6
Abstract
The origin of quasiconformal mappings, like that of conformal mappings, can be traced back to old cartography where the basic problem was the search for mappings from the sphere onto the plane with minimal deviation from conformality, subject to certain conditions which were made precise. In this paper, we survey the development of cartography, highlighting the main ideas
that are related to quasiconformality. Some of these ideas were completely ignored in the previous historical surveys on quasiconformal mappings. We then survey early quasiconformal theory in the works of Grötzsch, Lavrentieff, Ahlfors and Teichmüller, which are the 20th-century founders of the theory.