G. Khuskivadze and V. Paatashvili

A. Razmadze Mathematical Institute, Georgian Academy of Sciences Tbilisi, Georgia

A NOTE ON A CONFORMAL MAPPING OF SIMPLY CONNECTED DOMAINS WITH JORDAN BOUNDARIES

Let Γ_{0} be a Jordan piecewise smooth curve bounding a finite domain D_{0}, and Γ_{1} be the same curve having one common with Γ point; all the rest points lie in D_{0}. Denote by D a domain with the boundary Γ = Γ_{0} ∪ Γ_{1}.

The report states that for the case under consideration the analogue of Warschawski’s result on properties of a derivative, mapping conformally the unit circle onto D [1] (established for domains with Jordan piecewise Ljapunov curves), is valid.

References

1. S. E. Warschawski, Über dass Randverharten der Abletung der Abbildungsfunktion der Kanformer Abbildung. Math. Zeitschr. 35(1932), No. 3–4, 321–456.