ON THE CONVERGENCE OF CIRCLE PACKINGS TO THE QUASICONFORMAL MAP |
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Authors: | Huang Xiaojun Shen Liang |
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Affiliation: | aCollege of Mathematics and Physics, Chongqing University, Chongqing 400044, China;bInstitute of Mathematics, Academiy of Mathematics & System Sciences, Chinese Academiy of Sciences, Beijing 100190, China |
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Abstract: | Rodin and Sullivan (1987) proved Thurston's conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞. |
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Keywords: | circle packing quasiconformal map complex dilation2000 MR Subject Classification: 30C85 52C15 30C35 |
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