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Green\'s Mapping and Julia Sets
Ilia Binder, Paul F. X. M\"uller, Peter Yuditskii
https://arxiv.org/abs/2508.04207 https://arxiv.org/pdf/2508.0420…

Greenś Mapping and Julia Sets
In March 1999, the first named author (Binder) posed the problem of showing that a ``good direction'' $ψ\in [0,2]$ exists, for any Green's mapping $T:H\rightarrow\tilde Ω$, i.e., \begin{equation}\label{binder} \int\limits_0\limits^{1} |T''(re^{iπψ})|dr <\infty, \quad\text{ for at least one } \quad ψ\in [0,2]. \end{equation} Presently this problem is open even in the special case where $\partial Ω$ is a uniformly perfect subset of the real line. In this paper we obtain a posi…