科研之友
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摘要
For a fixed integer m = 2, let be an m-connected region in the Riemann sphere S2 whose complement S2 \ is a union of m disjoint closed disks _ Uj and let fj be quasisymmetric mappings defined on. Uj for j = 1, 2,..., m. We construct discrete conformal welding for based on the circle packing approach. We show that the discrete conformal welding mappings induced by circle packings converge uniformly on compact subsets to their continuous counterparts and that the corresponding discrete conformal welding curves converge uniformly to quasicircles determined by fj. This gives a constructive proof of the existence and uniqueness theorem for conformalwelding of finitely connected regions.
