Zemin Zhou
Abstract
It is shown that if f~μis an extremal quasi-conformal mapping of landslide type, then there exists an extremal quasi-conformal mapping f~μ with a Beltrami coefficient μ and a sub-domain G of the unit diskΔ,such that μ is Teichmiiller equivalent toμand satisfies μ (z)=0,■z∈G.
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It is shown that if f~μis an extremal quasi-conformal mapping of landslide type, then there exists an extremal quasi-conformal mapping f~μ with a Beltrami coefficient μ and a sub-domain G of the unit diskΔ,such that μ is Teichmiiller equivalent toμand satisfies μ (z)=0,■z∈G.
Key concepts: Extremal length, Conformal map, Mathematics, Unit disk, Type (biology), Domain (mathematical analysis), Quasiconformal mapping, Unit (ring theory)