摘要
The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.
本文是作者在多连通区域单叶函数领域研究成果的总结．文中给出：Ｖｉｌｌａｔ公式的两个极简单证明；多连通区域的Ｓｃｈｗａｒｚ公式，Ｐｏｉｓｓｏｎ公式，Ｐｏｉｓｓｏ－Ｊｅｎｓｅｎ公式；多连通区域解析函数一参族对参数的可微性定理；多连通区域单叶函数的变分定理和参数表示定理；一类泛函极值问题的解．
基金
高等学校博士学科专项科研基金
