2012/10/28 by Dmitri Prokhorov, Prokhorov, Dmitri
Mathematics · #30C35 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1210.7426
openalex publication_date 2012/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Loewner-Kufarev evolution produces asymptotics for mappings onto domains close to the unit disk or the exterior of the unit disk. We deduce variational formulae which lead to the asymptotic conformal welding for such domains. The comparison of mappings onto bounded and unbounded components of the Jordan curve establishes an asymptotic connection between driving functions in both versions of the Loewner-Kufarev equation and conformal radii of the two domains.