The Schwarz Lemma At The Boundary Of The Symmetrized Bidisc

The symmetrized bilisc G₂ is a bounded domain in C² defined by G₂:={?z₁+Z₂,z₁z₂?? C²:|z₁|<1,|z₂|<1,z₁,z₂ ? C}.The symmetrized bidisc G₂ is a bounded pseudoconvex domain in C² with non-smooth boundary and no strong pseudoconvex boundary point.In this paper,we study the boundary Schwarz lemma for holomorphic self-mappings of the symmetrized bidisc G₂.Because the symmetrized bidisc has no strong pseudoconvex boundary point,our bound-ary Schwarz lemma in the paper is much different from the earlier related results.This paper is divided into three chapters:Chapter ? gives background and outlines our research result for the Schwarz lemma at the boundary of the symmetrized bidisc;Chapter ? gives the preliminary konwledge of the Schwarz lemma at the boundary of the symmetrized bidisc;Chapter ? gives our detailed proof of the Schwarz lemma at the boundary of the symmetrized bidisc.