Holomorphic Removability of Julia Sets

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Let $f(z) = z^2 + c$ be a quadratic polynomial, with c in the Mandelbrot set. Assume further that both fixed points of f are repelling, and that f is not renormalizable. Then we prove that the Julia set J of f is holomorphically removable in the sense that every homeomorphism of the complex plane to itself that is conformal off of J is in fact conformal on the entire complex plane. As a corollary, we deduce that the Mandelbrot Set is locally connected at such c.
48 pages. 9 PostScript figures

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Dynamical Systems, Complex Variables

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http://salesiana.dossiersoluciones.com/handle/123456789/77910

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9812164
 http://arxiv.org/abs/math/9812164

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arXiv