Annales Academię Scientiarum Fennicę
Mathematica
Volumen 35, 2010, 389-404
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.
doi:10.5186/aasfm.2010.3525
Copyright © 2010 by Academia Scientiarum Fennica