关于退化拟共形映射的分类与边界对应

On the Type and Boundary Correspondence of Degenerate Quasiconformal Mappings

关键词:  退化  拟共形映射  分类  边界对应

Key words:  Degenerate  Quasiconformal mappings  Type  Boundary correspondence

摘要:

设D是一个边界Γ∈C_T²(0 < T≤1)的有界单连通域,复函数q(z)∈C_T¹(D),|q(z)|的法向导数在z∈Γ时不等于零而对z∈D成立|q(z)|≤1,且等号至多对z∈Γ成立.对于复伸张q(z)满足上述条件的Beltrami方程的分类及同胚解的边界对应进行了讨论.

Abstract:

Suppose that D is a simply connected region whose boundary Γ∈ C_T² (0 < T ≤ 1), the complex function q(z) ∈ C_T¹(D), normal derivative of|q(z)|does not equal to zero for z ∈Γ,and|q(z)| ≤ 1 for z ∈D where equality may hold only at z ∈Γ. Type and boundary correspondence of the homeomorphic solution of the Beltrami equation are discussed under above conditions of complex dilatation q(z).