Uniform domains on holomorphic curves

Author： Arbeláez Hugo   Chuaqui Martin   Sierra Willy  

Publisher： Taylor & Francis Ltd

E-ISSN： 1747-6941|60|7|1015-1031

ISSN： 1747-6933

Source： Complex Variables and Elliptic Equations, Vol.60, Iss.7, 2015-07, pp. : 1015-1031

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Abstract

We study a recent criterion for the injectivity of a holomorphic curve in , the strong form of which is shown to imply that the image in is a uniform surface. This concept is borrowed from geometric function theory in connection with quasidisks. We also obtain a two-point distortion theorem giving sharp estimates for the separation of images in terms of the hyperbolic distance in .

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