Abstract
We study integrability cases for the multiple Loewner differential equation which generates conformal mappings from the upper half-plane $$\mathbb{H}$$ of the complex plane with multiple slits onto $$\mathbb{H}$$ . The research is reduced to constant, square root and exponential driving functions of the Loewner equation. Moreover, conformal mappings from $$\mathbb{H}$$ minus symmetric circular curves emanating from the joint point at the origin, onto $$\mathbb{H}$$ , are represented as solutions to the multiple Loewner equation. The results supplement earlier descriptions for single slit mappings given by Kager, Nienhuis and Kadanoff.
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