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The Löwner-Kufarev evolution produces asymptotics for mappings onto domains close to the unit disk $$\mathbb{D }$$ or the exterior of $$\mathbb{D }$$ . 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 Löwner-Kufarev equation and conformal radii of the two domains.
Computational Methods and Function Theory – Springer Journals
Published: Jan 23, 2013
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