On the computational complexity of the Riemann mapping. Binder, I., Braverman, M., & Yampolsky, M. Ark. Mat., 45(2):221–239, 2007.
On the computational complexity of the Riemann mapping [link]Paper  doi  bibtex   
@ARTICLE{BBY07a,
  author = {Binder, Ilia and Braverman, Mark and Yampolsky, Michael},
  title = {On the computational complexity of the {R}iemann mapping},
  journal = {Ark. Mat.},
  year = {2007},
  volume = {45},
  pages = {221--239},
  number = {2},
  coden = {AKMTAJ},
  doi = {10.1007/s11512-007-0045-x},
  file = {BBY07a.pdf:BBY07a.pdf:PDF},
  fjournal = {Arkiv f\"or Matematik},
  issn = {0004-2080},
  keywords = {bib,cca},
  mrclass = {03D78 (03D15 30C30 30F10 68Q17)},
  mrnumber = {2342601 (2010b:03055)},
  mrreviewer = {Timothy H. McNicholl},
  owner = {Vasco},
  timestamp = {2013.12.01},
  url = {http://dx.doi.org/10.1007/s11512-007-0045-x}
}

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