A characteristic parameter α_D of a domain D in R^n is introduced. D is unifonm if and only if α_D<∞. And α_D=1 if D is a ball or a half space. It is proved that the decomposability and the uniformity of a doma...A characteristic parameter α_D of a domain D in R^n is introduced. D is unifonm if and only if α_D<∞. And α_D=1 if D is a ball or a half space. It is proved that the decomposability and the uniformity of a domain in R^n are still equivalent. Some problems on uniform domains and decomposition domains are discussed.展开更多
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'...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.展开更多
文摘A characteristic parameter α_D of a domain D in R^n is introduced. D is unifonm if and only if α_D<∞. And α_D=1 if D is a ball or a half space. It is proved that the decomposability and the uniformity of a domain in R^n are still equivalent. Some problems on uniform domains and decomposition domains are discussed.
文摘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.
