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Regularity and extremality of quasiconformal homeomorphisms on CR 3-manifolds. (English) Zbl 0880.32010
The regularity of conformal homeomorphisms is studied on smooth locally embeddable strongly pseudoconvex CR (= Cauchy-Riemann) manifolds. Then the maximal dilatations of quasiconformal homeomorphisms are estimated in terms of the moduli of curve families. The extremal quasiconformal mappings are constructed in the paper in some homotopy classes on some CR three-manifolds: the CR circle bundles over flat tori. Finally, the analogy of the mappings in question and the familiar Teichmüller mappings on Riemann surfaces is discussed.

##### MSC:
 32G07 Deformations of special (e.g., CR) structures 32V99 CR manifolds 30C65 Quasiconformal mappings in $$\mathbb{R}^n$$, other generalizations 32T99 Pseudoconvex domains
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