3 problems

Let $\Omega$ be an $n$-connected domain. For each $z\in\Omega$ and each $1\leq k\leq n$, let $\varphi_{z,k}$ be a canonical mapping associated with the boundary component indexed b…

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 ma…

Let $\Omega\subset\mathbb{C}$ be a finitely connected domain with disjoint boundary components $\gamma_0,\gamma_1,\ldots,\gamma_n$, where $\gamma_0=\partial\mathbb{D}$ and the rema…