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On Differentiability at the Boundary in Conformal Mapping

Name: On Differentiability at the Boundary in Conformal Mapping
Creator: S. E. Warschawski
Keywords: complex functions, 4. Education, 16. Peace & justice

On differentiability at the boundary in conformal mapping

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Aug 1961Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 12, page 614 (issn: 0002-9939,

Authors: S. E. Warschawski;

doi: 10.2307/2034255 , 10.1090/s0002-9939-1961-0131524-8

On Differentiability at the Boundary in Conformal Mapping

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Abstract

Introduction. The object of this note is to present a short and simple proof of the following two theorems. THEOREM 1. Suppose that C is a closed rectifiable Jordan curve in the complex c-plane and that C has a continuously turning tangent in a neighborhood of one of its points, Po. Suppose, furthermore, that the tangent angle r(s) as function of the arc length s has a modulus of continuity w(t) at the point so which corresponds to Po, i.e.,

Keywords

complex functions

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