Holomorphic Removability of Julia Sets

Details Holomorphic Removability of Julia Sets Holomorphic Removability of Julia Sets

1998-12-31

arxiv.org/abs/math/9812164v1

Mathematics

Dynamical Systems

48 pages. 9 PostScript figures

Scientific paper

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.

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