中文摘要：

设B^n为n维复单位球,U^m为m维多圆柱,本文利用全纯自同构将边界映为边界的这一性质．得到了乘积域B^n×U^m的全纯自同构的一些必要条件．再从这些必要条件出发．成功找到了乘积域B^n×U^m的全部全纯自同构．在总的思路上,本篇文章采用的是类似于得到单复变中单位圆盘的Aut（U）的方法．即把零点映为零点的全纯自同构（类似于单复变函数论中的旋转变换）与一类特殊的全纯自同构（类似于单复变函数论中的Moebius变换）复合．

英文摘要：

In this article, some requirements of homomorphic automorphism of the domain B^n×U^m were found by using the property that homomorphie automorphism turns the border into the border. With those requirements, Aut（B^n×U^m） was found successfully. The main thread of the article was the same way as Aut（U） in one complex variable. It is Composed by two special homomorphic automorphisms,one maps zero to zero,the other is analogous to Moebius transformation in one complex variable.