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Quasiconformal mappings on the Heisenberg group: an overview. (English) Zbl 1345.30063

Papadopoulos, Athanase (ed.), Handbook of Teichmüller theory. Volume VI. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-161-3/hbk; 978-3-03719-661-8/ebook). IRMA Lectures in Mathematics and Theoretical Physics 27, 375-393 (2016).
This is Chapter 11 of [A. Papadopoulos (ed.), Handbook of Teichmüller theory. Volume VI. Zürich: EMS (2016; Zbl 1330.30012)].
From the introduction to this book: Chapter 11 by Ioannis Platis concerns the theory of quasiconformal mappings of the Heisenberg group. This theory started in the 1980s in works of Korányi-Reimann and of Pansu, it underwent various developments, and it is still an active field of research. In several ways, it is a generalization of the quasiconformal theory of surfaces studied in Teichmüller theory. Like in the classical surface case, there are several definitions of quasiconformal mappings \([\ldots]\)
For the entire collection see [Zbl 1344.30001].

MSC:

30F60 Teichmüller theory for Riemann surfaces
30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
30-02 Research exposition (monographs, survey articles) pertaining to functions of a complex variable
32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces

Citations:

Zbl 1330.30012
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