Boundary Uniqueness Theorems On Several Types Of Domains

Boundary uniqueness theorem first arises in the study of boundary Schwarz lemma.In 1994,Burns-Krantz established a new Schwarz lemma at the boundary which is exactly the boundary uniqueness theorem we are going to study.This thesis is a study on boundary uniqueness theorem.The main work of this paper is to generalize the boundary uniqueness theorems from equidimensional cases to nonequidimensional ones.Two types of domains are chosen in this paper.One is the unit ball in several complex variables Bn = ?(z1,z2,…,zn)? Cn:?in=1|zi|2?1},which is a bounded smooth strongly convex domain,strongly pseudoconvex domain and homogeneous domain;the other is the Fock-Bargmann-Hartogs domain Dn,m ={(z,w)? Cn × Cm:||z||2<e?|w||2,??0},which is an unbounded pseudoconvex nonhomogeneous domain.The paper focuses on a type of boundary uniqueness theorem established by Burns-Krantz,and we work out some nonequidimensional results of their theorem on the unit ball.Also other kinds of Burns-Krantz type theorems on the unit ball and Fock-Bargmann-Hartogs domain obtained by some men of mathematics are generalized to nonequidimensional results.Firstly,the paper introduces some background contents and necessary primary knowledges of boundary Schwarz lemma and boundary uniqueness theorem.Secondly,this paper presents some known results which are for generalizations or references.Finally,the main results and their proofs are written in this paper.