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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This work was funded by the Russian Science Foundation (project no. 17-11-01229).
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(Submitted by F. G. Avkhadiev)
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Prokhorov, D. Exact Solutions of the Multiple Loewner Equation. Lobachevskii J Math 41, 2248–2256 (2020). https://doi.org/10.1134/S1995080220110189
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DOI: https://doi.org/10.1134/S1995080220110189