Computational Methods and Function Theory 10 (2010), No. 1, 35--47
Copyright Heldermann Verlag 2010
Tobias Kaiser
tobias.kaiser@uni-passau.de , Universität Passau, Fakultät für Informatik und Mathematik, 94030 Passau, Germany.
We say that a simply connected domain in the complex plane has an analytic cusp at the origin if its boundary at the origin is given by two regular analytic curves which form a cusp. We investigate the asymptotic behaviour of a conformal map onto the upper half plane at the origin. Therefore we introduce the notion of an analytic cusp with small perturbation of angles. Assuming this condition we determine the asymptotic behaviour in terms of a holomorphic function and give upper bounds for the derivatives of the mapping function.
Keywords: Riemann Mapping Theorem, asymptotic behaviour, analytic cusp.
MSC 2000: 30C20, 30E15, 14P15.
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