塌陷型极值拟共形映射的性质

On Extremal Quasi-conformal Mappings of Landslide Type

证明了如果f~μ是单位圆△上塌陷型极值拟共形映射,则存在与f~μ等价的极值拟共形映射f^(?)以及单位圆的子区域G,使得面(z)=0,(?)z∈G.

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.