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arXiv · 2302.04350

One-parameter families of conformal mappings of the half-plane onto polygonal domains with several slits

A. Posadskii·S. Nasyrov
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Abstract

Among various methods of finding accessory parameters in the Schwarz-Christoffel integrals, Kufarev's method, based on the Loewner differential equation, plays an important role. It is used for describing one-parameter families of functions that conformally map a canonical domain onto a polygon with a slit the endpoint of which moves along a polygonal line starting from a boundary point. We present a modification of Kufarev's method for the case of several slits, the lengths of which have depend of each other in a certain way. We justify the method and find a system of ODEs describing the dynamics of accessory parameters. We also present the results of numerical calculations which confirm the efficiency of our method.

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A. Posadskii, S. Nasyrov. 2023-02-08. One-parameter families of conformal mappings of the half-plane onto polygonal domains with several slits. https://arxiv.org/abs/2302.04350

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