The Schwarz Lemma At The Boundary Of The Non-convex Complex Ellipsoids B_2,p

Let EP1,P2 = {z ∈Cn:|z|p1 + |z2|p2 +…+|Zn|p2<1},(p1>1,p2>1)be an egg domain in Cn Recently,Tang-Liu established a new type of classical boundary Schwarz lemma.Let B2,p ={z∈C2:|z1|2 + |z2|p<1}(0<p<1).Then B2,p is a non-convex complex ellipsoid in C2 without smooth boundary.In this paper,we establish a new type of classical boundary Schwarz lemma at z0 ∈(?)B2,p for holomorphic self-mappings of B2,p,where z0 is any smooth boundary point of B2,p.This paper is divided into three chapters:Chapter Ⅰ gives background and outlines our research result for boundary Schwarz lemma;Chapter Ⅱ gives the preliminary knowledge of the boundary Schwarz lemma;Chapter Ⅲ gives our detailed proof of the boundary Schwarz lemma for holomorphic self-mappings of B2,p.