Slodkowski定理的Chirka证明的一些注解(英文)

通过在一个积分算子上运用Schauder不动点定理,Chirka对Slokowski的全纯运动扩张定理提供了一个优美的简单证明.本文中,作者对构造此证明的启发提供一个参考同时用此方法通过不同方式来构造全纯扩张.一个自然的问题是研究这些用不同方式得到的全纯扩张是否相同.因此对全纯扩张唯一性已有的判断法提供一个简单的综述.最后介绍在全纯扩张唯一性存在时的一个应用.

Remarks on Chirka's Proof of Slodkowski's Theorem

By applying Schauder's fixed point theorem to an integral operator,Chirka developed a remarkably simple proof for Slodkowski's theorem on extending holomorphic motions. In this paper,we first present our understanding of a motive for designing the integral operator, from which we also recapitulate the main work in Chirka's proof.When applying Chirka's operator in different ways to obtain the extensions of holomorphic motions,a question on the uniqueness of extensions arises.After a brief summary on some kno...