Regularity And Extremality Of Quasiconformal Homeomorphisms On CR 3-Manifolds

1993/12/30 by Puqi Tang, Tang, Puqi
Mathematics · #32 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32

paper · pdf · doi:10.48550/arxiv.math/9312202

arxiv created 1993/12/30 · arxiv updated 2009/11/30

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.

Related

• Quasiconformal Homeomorphisms on CR 3-Manifolds With Symmetries
• On the regularity of CR mappings in higher codimension
• Distortion of quasiconformal mappings with identity boundary values
• Existence of quasiconformal maps with maximal stretching on any given countable set
• The existence of quasiconformal homeomorphism between planes with countable marked points