English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Andreev-Thurston Circle Packing Theorem is generalized to packings ofconvex bodies in planar simply connected domains. This turns out to be a usefultool for constructing conformal and quasiconformal mappings with interestinggeometric properties. We attempt to illustrate this with a few results aboutuniformizations of finitely connected planar domains. For example, thefollowing variation of a theorem by Courant, Manel and Shiffman is proved andgeneralized. If $G$ is an $n+1$-connected bounded planar domain, $H$ is asimply connected bounded planar domain, and $P_1,P_2,...,P_n$ are (compact)planar convex bodies, then sets $P_j'$ can be found so that $G$ is conformallyequivalent to $H-\cup_{j=1}^n P_j'$, and each $P_j'$ is either a point, or ispositively homothetic to $P_j$.

Combinatorically Prescribed Packings and Applications to Conformal and Quasiconformal Maps