The circularly slit disk formula for the squeezing function

Let $\Omega\subset\mathbb C$ be an $m$-connected domain without degenerate boundary components. For each $z\in\Omega$ and $j=0,\ldots,m-1$, let $f_{z,j}$ be the unique conformal map of $\Omega$ onto a circularly slit disk normalized by $f_{z,j}(z)=0$, $f'_{z,j}(z)>0$, and $f_{z,j}(\Gamma_j)=\partial\mathbb D$, where $\Gamma_0,\ldots,\Gamma_{m-1}$ are the boundary components of $\Omega$. Circularly slit disk formula. The squeezing function should satisfy

$$S_\Omega(z)=\max_{j=0,\ldots,m-1}{\mathsf{dist}}\bigl(0,\partial f_{z,j}(\Omega)\bigr).$$

The squeezing function measures how large a disk centered at the image of a point can be embedded in a normalized injective image of the domain inside the unit disk. The conjecture asserts that, for finitely connected planar domains without degenerate boundary components, this optimum is attained by one of the canonical conformal maps onto a circularly slit disk; its resolution status is not specified in the supplied source context.