Annales Academię Scientiarum Fennicę

Mathematica

Volumen 35, 2010, 389-404

# TREE-LIKE DECOMPOSITIONS AND CONFORMAL MAPS

## Christopher J. Bishop

SUNY at Stony Brook, Department of Mathematics

Stony Brook, NY 11794-3651, U.S.A.; bishop 'at' math.sunysb.edu

**Abstract.**
Any simply connected rectifiable domain
\Omega can be decomposed into uniformly
chord-arc subdomains
using only crosscuts of the domain.
We show that such a decomposition allows one to construct a
map from \Omega to the
disk which is close to conformal in a uniformly quasiconformal sense.
This answers a question of Vavasis.

**2000 Mathematics Subject Classification:**
Primary 30C35; Secondary 30C30, 65E05, 30C62.

**Key words:**
Conformal mapping, quasiconformal maps,
inner chord-arc
domains, numerical conformal mapping, hyperbolic geometry,
Schwarz-Christoffel formula.

**Reference to this article:** C.J. Bishop:
Tree-like decompositions and conformal maps.
Ann. Acad. Sci. Fenn. Math. 35 (2010), 389-404.

Full document as PDF file

doi:10.5186/aasfm.2010.3525

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