We show that, given a non-degenerate, finitely connected domain D, its boundary, and the number of its boundary components, it is possible to compute a conformal mapping of D onto a circular domain without prior knowledge of the circular domain. We do so by computing a suitable bound on the error in the Koebe construction (but, again, without knowing the circular domain in advance). Recent resu...

We study Koebe orderings of planar graphs: vertex obtained by modelling the graph as intersection pairwise internally-disjoint discs in plane, and ordering vertices non-increasing radii associated discs. prove that for every $d\in \mathbb{N}$, any such has $d$-admissibility bounded $O(d/\ln d)$ weak $d$-coloring number $O(d^4 \ln d)$. This particular shows graphs is d)$, which asymptotically ma...

The classical Schwarz-Christoffel transformation provides a formula for the conformal mapping of the half-plane onto a plane polygon. A generalization enlarging the class of image domains to include many-sheeted plane polygons with interior winding points was known already to at least Schwarz and Schlifli.' This note is concerned with a further simple extension of the formula which delivers a u...