The Convergence of Circle Packings to the Riemann Mapping
نویسندگان
چکیده
منابع مشابه
0 Conformally symmetric circle packings . A generalization of Doyle spirals
Circle packings (and more generally patterns) as discrete analogs of conformal mappings is a fast developing field of research on the border of analysis and geometry. Recent progress was initiated by Thurston’s idea [T] about the approximation of the Riemann mapping by circle packings. The corresponding convergence was proven by Rodin and Sullivan [RS]; many additional connections with analytic...
متن کاملOn the Convergence of Circle Packings to the Riemann Map
Rodin and Sullivan (1987) proved Thurston’s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby providing a refreshing geometric view of Riemann’s Mapping Theorem. We now present a new proof of the Rodin–Sullivan theorem. This proof is based on the argument principle, and has the following virtues. 1. It applies to more general packings. The Ro...
متن کاملHexagonal circle patterns and integrable systems. Patterns with constant angles
The theory of circle packings and, more generally, of circle patterns enjoys in recent years a fast development and a growing interest of specialists in complex analysis and discrete mathematics. This interest was initiated by Thurston’s rediscovery of the Koebe-Andreev theorem [K] about circle packing realizations of cell complexes of a prescribed combinatorics and by his idea about approximat...
متن کاملPatterns with constant angles
The theory of circle packings and, more generally, of circle patterns enjoys in recent years a fast development and a growing interest of specialists in complex analysis and discrete mathematics. This interest was initiated by Thurston’s rediscovery of the Koebe-Andreev theorem [K] about circle packing realizations of cell complexes of a prescribed combinatorics and by his idea about approximat...
متن کاملDiscrete Z and Painlevé equations
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...
متن کامل