2002/03/27 by Steven R. Bell, Bell, Steven R.
Mathematics · #30C40 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:30C40
paper · pdf · doi:10.48550/arxiv.math/0203280
arxiv created 2002/03/27 · openalex publication_date 2002/03/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is proved that the family of Ahlfors extremal mappings of a multiply connected region in the plane onto the unit disc can be expressed as a rational combination of two fixed Ahlfors mappings in much the same way that the family of Riemann mappings associated to a simply connected region can be expressed in terms of a single such map. The formulas reveal that this family of mappings extends to the double as a real analytic function of both variables. In particular, the infinitesimal Caratheodory metric will be expressed in strikingly simple terms. Similar results are proved for the Green's function, the Poisson kernel, and the Bergman kernel.