Holomorphic Removability of Julia Sets
| dc.creator | Kahn, Jeremy | |
| dc.date | 1998-12-31 | |
| dc.date.accessioned | 2026-07-07T05:27:25Z | |
| dc.date.available | 2026-07-07T05:27:25Z | |
| dc.description | 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. | |
| dc.description | 48 pages. 9 PostScript figures | |
| dc.identifier | https://arxiv.org/abs/math/9812164 | |
| dc.identifier | http://arxiv.org/abs/math/9812164 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77910 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.title | Holomorphic Removability of Julia Sets | |
| dc.type | text |