Computational Methods and Function Theory 4 (2004), No. 1, 111--126
Copyright Heldermann Verlag 2004
Tom Carroll
t.carroll@ucc.ie , Department of Mathematics, National University of Ireland, Cork, Ireland.
Walter K. Hayman
Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, U.K.
By a parabola-shaped domain we mean a planar domain lying between the curves y = xα and y = -xα, the case α = 1/2 corresponding to the standard parabola. We obtain asymptotic estimates for conformal mappings of such domains onto standard regions, and for the derivatives of such maps.
Keywords: Conformal mapping, distortion, Dini-smooth domain.
MSC 2000: Primary 30C20.
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