Matching univalent functions and conformal welding

Details Matching univalent functions and conformal welding Matching univalent functions and conformal welding

2008-06-05

arxiv.org/abs/0806.0930v1

Mathematics

Complex Variables

17 pages

Scientific paper

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.

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