摘要
In this paper, we consider the following Reinhardt domains. Let M = (M1, M2,..., Mn) : [0,1] → [0,1]^n be a C2-function and Mj(0) = 0, Mj(1) = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′(r) 〈 C2jr^pj-1, r∈ (0, 1), pj 〉 2, 1 ≤ j ≤ n, 0 〈 C1j 〈 C2j be constants. Define DM={z=(z1,z2,…,Zn)^T∈C^n:n∑j=1 Mj(|zj|)〈1}Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f : DM -→ C^n.
In this paper, we consider the following Reinhardt domains. Let M = (M1, M2,..., Mn) : [0,1] → [0,1]^n be a C2-function and Mj(0) = 0, Mj(1) = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′(r) 〈 C2jr^pj-1, r∈ (0, 1), pj 〉 2, 1 ≤ j ≤ n, 0 〈 C1j 〈 C2j be constants. Define DM={z=(z1,z2,…,Zn)^T∈C^n:n∑j=1 Mj(|zj|)〈1}Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f : DM -→ C^n.
基金
the Natural Science Foundation of China (Grant No.10671194 and 10731080/A01010501)