# Conformal mappings onto domains with arbitrarily specified boundary shapes

@article{Harrington1982ConformalMO, title={Conformal mappings onto domains with arbitrarily specified boundary shapes}, author={A. N. Harrington}, journal={Journal d’Analyse Math{\'e}matique}, year={1982}, volume={41}, pages={39-53} }

#### 16 Citations

Uniformization by rectangular domains: A path from slits to squares

- Mathematics
- 2020

Abstract Let Σ ( Ω ) be the class of functions f ( z ) = z + a 1 z + ⋯ univalent on a finitely connected domain Ω, ∞ ∈ Ω ⊂ C ‾ . By a classical result due to H. Grotzsch, the function f 0 maximizing… Expand

Domain-filling circle packings

- Mathematics
- 2019

According to a classical theorem of Constantin Caratheodory, any Jordan domain G admits a unique conformal mapping onto the unit disk $$\mathbb {D}$$ such that three distinguished boundary points of… Expand

Algebraicity regarding Graphs and Tilings

- 2018

Given a planar graph G, we prove that there exists a tiling of a rectangle by squares such that each square corresponds to a face of the graph and the side lengths of the squares solve an extremal… Expand

Notes on Hilbert's 16th: experiencing Viro's theory

- Mathematics
- 2013

This text is intended to become in the long run Chapter 3 of our long saga dedicated to Riemann, Ahlfors and Rohlin. Yet, as its contents evolved as mostly independent (due to our inaptitude to… Expand

Ahlfors circle maps and total reality: from Riemann to Rohlin

- Mathematics
- 2012

This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the… Expand

Planar relative Schottky sets and quasisymmetric maps

- Mathematics
- 2012

A relative Schottky set in a planar domain D is a subset of D obtained by removing from D open geometric discs whose closures are in D and are pairwise disjoint. In this paper we study quasisymmetric… Expand

Oded Schramm: From Circle Packing to SLE

- Mathematics
- 2010

When I first met Oded Schramm in January 1991 at the University of California, San Diego, he introduced himself as a “Circle Packer”. This modest description referred to his Ph.D. thesis around the… Expand

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It is the object of this paper to set forth a proof of Theorem 1 below, to the effect that an arbitrary plane region D bounded by a finite number of mutually disjoint Jordan curves can be mapped one… Expand

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