复空间中若干域之间的双全纯等价  

Biholomorphic equivalence between several domains in a complex space

作　　者：程晓亮[1] 马会波 CHENG Xiao-liang;MA Hui-bo(College of Mathematics,Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《吉林师范大学学报（自然科学版）》2022年第2期62-66,共5页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(12026420)。

摘　　要：对于复空间中的n维单位球B_(n)和n维单位圆柱U_(n),利用反证法,通过构造乘积域B_(n)×U_(n)上的凸映射,根据凸映射和可递域的性质,验证了由假设构造的映射不能将单位球B_(n)映为乘积域B_(n)×U_(n),从而证明了单位球B_(n)与乘积域B_(n)×U_(n)不双全纯等价.For the n-dimensional unit ball B_(n) and n-dimensional unit polydisk U_(n)in complex space,by using the method of counter proof,by constructing the convex mapping on the product domain B_(n)×U_(n),according to the properties of convex mapping and transitive field,it was verified that the mapping constructed by hypothesis could not map the unit ball B_(n) into the product domain B_(n)×U_(n),so it was proved that the unit ball B_(n) and the product domain B_(n)×U_(n) were not biholomorphic equivalent.

关 键 词：双全纯等价 多复变 自同构群 凯莱变换 

分 类 号：O186[理学—数学]