【摘要】 <正> §1.内容的简单介绍当试把Schwarz引理推广到多个复变数论者,曾有H.Cartan,Carathéo-dory,Bergmann,Bochner-Martin,Bureau,Фукс,Ozaki-Kashiwagi-Tsuboi,Sthr.但从这许多的前人之结果中,仍然使人产生一问题,就是Schwarz 引理能否推广与在什么意义下能推广.更多还原

【Abstract】 In this paper the author gives a complete and detailed proof of the re-sults announced in Science Record,New set.vol.Ⅰ.No.2（1957）,6—9.Besides,there are generalizations and consequences of the previousresults,i.e.1°If a bounded schlicht domain D is transitive,there exists a posi-tive constant κ depending only on D such that for any bounded schlichtdomain D and any analytic mapping w=f（z）carrying D into D we al-ways have（?）2°If D is a bounded schlicht transitive domain and if there is al-ways a unique geodesic passing through any two points of D,then,for anytwo points z₁,z₂ ∈（?）and any inner analytic mapping carrying z₁,z to w₁,w₂ respectively,we always havewhere x（z₁,z₂）is the geodesic distance between z₁ and z₂,and κ₀（?）theSchwarz constant of D¹).3°If R is the topology product of the classical domains （?）^（1）,（?）^（2）,…,R^（j）,i.e.R=（?）^（1）×R^（2）×…×R^（j）,then the Schwarz constant ofR satisfies the relation（?）更多还原