2008/06/05 by Erlend Grong, Grong, Erlend, Pavel Gumenyuk +4
Mathematics · Physics and Astronomy · #17B68 #30C35 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math-ph #math.CV #math.MP #math.RT #msc:17B68 #msc:30C35
paper · pdf · doi:10.48550/arxiv.0806.0930
17 pages
arxiv created 2008/06/05 · openalex publication_date 2008/06/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a conformal mapping f of the unit disk \mathbb D onto a simply connected domain D in the complex plane bounded by a closed Jordan curve, we consider the problem of constructing a matching conformal mapping, i.e., the mapping of the exterior of the unit disk \mathbb D^* onto the exterior domain D^* regarding to D. The answer is expressed in terms of a linear differential equation with a driving term given as the kernel of an operator dependent on the original mapping f. Examples are provided. This study is related to the problem of conformal welding and to representation of the Virasoro algebra in the space of univalent functions.