Discrete Zγ and Painlevé Equations

  title={Discrete Zγ and Painlev{\'e} Equations},
  author={Sergey I. Agafonov and Alexander I. Bobenko},
Circle patterns as discrete analogs of conformal mappings is a fast-developing field of research on the border of analysis and geometry. Recent progress in their investigation was initiated by Thurston’s idea (see [18]) about approximating the Riemann mapping by circle packings. The corresponding convergence was proven by Rodin and Sullivan in [15]. For hexagonal packings, it was established by He and Schramm in [9] that the convergence is C∞ . Classical circle packings comprised by disjoint… CONTINUE READING
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