关于万有Teichmüller空间两个性质的简洁证明

The Concise Proofs of Two Properties of the Universal Teichmüller Space

根据[fv]=12-vzz2∈L,给出了魏寒柏"关于万有Teichmüller空间T1的分支"一文中定理2.1的简洁证明;构造了具体的解析函数fλ(z),使其当λ>0时:fλ∈L0,当λ<0时:fλ∈Lθ,从而简化了王哲"The Distance be-tween Different Component of the Universal Teichmüller Space"一文中定理2.2的证明.

For theorem 2.1 of Wei Han - bai＇s paper The component of the university Teichmǖller space T1 , qccording to[fυ]= 2υz/1-z^2∈ L, we give the concise proof. For theorem 2.2 of Wang zhe＇s paper The distance between different component of the universal TeichmiZller space , by means of one holomorphic function fλ （z） which satisfies ：when λ 〉 0, then [fλ ] ∈ L0, when λ〈 0, then [fλ ] ∈ L0, one concise proof is obtained.