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On the estimates of hyperbolic area distortion of quasiconformal mappings. (English) Zbl 1174.30021

Summary: The distortion property of the hyperbolic area of planar quasiconformal mappings is studied in this paper. In the case of radial quasiconformal mappings and angular deformed quasiconformal mappings, their hyperbolic area distortions are estimated quite sharply. The result can be applied to judge whether the hyperbolic area of a planar subset is explodable.

MSC:

30C62 Quasiconformal mappings in the complex plane