数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1173-1181.doi: 10.1016/S0252-9602(09)60095-3
黄小军, 沈良
HUANG Xiao-Jun, CHEN Liang
摘要:
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 ∞.
中图分类号: