Regularity And Extremality Of Quasiconformal Homeomorphisms On CR 3-Manifolds

Abstract

This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve families are used to estimate the maximal dilatations of quasiconformal homeomorphisms. On certain CR 3-manifolds, namely, CR circle bundles over flat tori, extremal quasiconformal homeomorphisms in some homotopy classes are constructed. These extremal mappings have similar behaviors to Teichmüller mappings on Riemann surfaces.

References in corpus (1)

• Quasiconformal Homeomorphisms on CR 3-Manifolds With Symmetries

Cited by in corpus (4)

• Rigidity of fiber-preserving quasisymmetric maps
• Stability of isometric maps in the Heisenberg group
• Moduli of Legendrian foliations and quadratic differentials in the Heisenberg group
• Quadratic differentials in spherical CR geometry