Factorisation of conformal maps on finitely connected domains

Benjamin Doyon

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arXiv · 1107.0582

Factorisation of conformal maps on finitely connected domains

Benjamin Doyon

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Abstract

Let $U$ be a multiply connected domain of the Riemann sphere $\hat{C}$ whose complement $\hat{C}\setminus U$ has $N<\infty$ components. We show that every conformal map on $U$ can be written as a composition of $N$ maps conformal on simply connected domains. This improves on a recent result of D.E. Marshall, but our proof uses different ideas, and involves the uniformisation theorem for Riemann surfaces.

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Benjamin Doyon. 2011-07-04. Factorisation of conformal maps on finitely connected domains. https://arxiv.org/abs/1107.0582

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