The Structure Of The Proper Holomorphic Rational Mappings Between Unit Balls In Several Complex Variables

This paper mainly studies the construction of proper holomorphic mappings between unequal dimensional unit balls in several complex variables.Based on the proper holomorphic mappings between unit balls and their existing explicit expressions,some new higher dimensional proper holomorphic mappings between unit balls are constructed by tensor product and direct sum decomposition,and the new explicit expressions are obtained.This paper is divided into four chapters.The first chapter mainly introduces the basic definitions of the holomorphic mappings and the proper holomorphic mappings,and introduces the equivalent lemma of the proper holomorphic mappings of bounded domains and its proof process.The second chapter introduces the proper holomorphic mapping between the unit disks is a finite Blaschke product,and discusses the automorphism group of the unit polydisk and the unit ball.The third chapter introduces the gap interval of the proper holomorphic rational mappings between unit balls,classifies and summarizes the proper holomorphic rational mappings between unit balls in different gap intervals,and gives the explicit expressions of the equivalent mappings.The fourth chapter mainly uses the proper holomorphic mappings from the unit ballB² toB⁴、Bⁿ toB^2n-1、Bⁿ toB^3n-3and their explicit expressions given in the third chapter to construct the new higher dimensional proper holomorphic mappings between unit balls by tensor product and direct sum decomposition,and then obtains higher dimensional explicit expressions.