Geodesic
Boundary behavior of derivatives of conformal mappings of simply connected domains
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2014), pp. 29-35
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Conformal mappings of simply connected domains $G$ on a disc or a halfplane are considered in the case when boundaries consist of smooth boundary arcs $\Gamma$ reachable from inside of $G$. Sufficient conditions for existence of angular limit of the derivative of such mappings and its boundedness at some given boundary point are found. A sufficient condition of existence of a bounded derivative on the region's boundary is given as a corollary. 
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E. P. Dolzhenko; S. V. Kolesnikov. Boundary behavior of derivatives of conformal mappings of simply connected domains. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2014), pp. 29-35. http://geodesic.mathdoc.fr/item/VMUMM_2014_5_a4/

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