Conformally Symmetric Circle Packings: A Generalization of Doyle's Spirals
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...
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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...
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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...
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Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain Ω in a compact Riemann surface S. This means that each connected component B of S \ Ω is either a point or a closed geometric disc with respect to the complete constant curvature conformal metric of the Riemann surface (Ω ∪ B). Moreover...
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The Andreev-Thurston Circle Packing Theorem is generalized to packings of convex bodies in planar simply connected domains. This turns out to be a useful tool for constructing conformal and quasiconformal mappings with interesting geometric properties. We attempt to illustrate this with a few results about uniformizations of finitely connected planar domains. For example, the following variatio...
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ورودعنوان ژورنال:
- Experimental Mathematics
دوره 10 شماره
صفحات -
تاریخ انتشار 2001