Huang Xiaojun1; Shen Liang2
Source Publicationactamathematicascientia
AbstractRodin 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 infinity.
Funding Project[National Natural Science Foundation of China] ; [Chongqing Natural Science Foundation]
Document Type期刊论文
Recommended Citation
GB/T 7714
Huang Xiaojun,Shen Liang. ontheconvergenceofcirclepackingstothequasiconformalmap[J]. actamathematicascientia,2009,29(5):1173.
APA Huang Xiaojun,&Shen Liang.(2009).ontheconvergenceofcirclepackingstothequasiconformalmap.actamathematicascientia,29(5),1173.
MLA Huang Xiaojun,et al."ontheconvergenceofcirclepackingstothequasiconformalmap".actamathematicascientia 29.5(2009):1173.
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