1993/12/30 by Puqi Tang, Tang, Puqi
Mathematics · #32 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32
paper · pdf · doi:10.48550/arxiv.math/9312201
arxiv created 1993/12/30 · openalex publication_date 1993/12/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An extremal quasiconformal homeomorphisms in a class of homeomorphisms between two CR 3-manifolds is an one which has the least conformal distortion among this class. This paper studies extremal quasiconformal homeomorphisms between CR 3-manifolds which admit transversal CR circle actions. Equivariant K-quasiconformal homeomorphisms are characterized by an area-preserving property and the K-quasiconformality of their quotient maps on the spaces of S1-orbits. A large family of invariant CR structures on S3 is constructed so that the extremal quasiconformal homeomorphisms among the equivariant mappings between them and the standard structure are completely determined. These homeomorphisms also serve as examples showing that the extremal quasiconformal homeomorphisms between two invariant CR manifolds are not necessarily equivariant.