Applications holomorphes propres entre certains domaines bornés de ℂn

Fatou and Korányi-Vági type theorems on the minimal ball

“…Moreover B * is neither homogeneous nor Reinhardt (see [5], [13]). Function theory on the minimal ball was studied by several authors (see [12], [14], [15], [8], [7], [18]). In his recent work [19], E. H. Youssfi developed a method for computing the Bergman and Szegö kernel of a new class of pseudoconvex domains including the minimal ball.…”

Proper holomorphic self-mappings of the minimal ball

“…We can repeat the same argument used in the proof of Proposition 1 (second case) to show that there is no proper holomorphic mapping from the minimal ball onto a strongly pseudoconvex bounded domain in C n with C 2 boundary. The problem of existence of proper holomorphic mappings from a strongly pseudoconvex bounded domain in C n (n ≥ 3) with C 2 boundary onto the minimal ball was answered in the negative in [11]. These results solve a question raised by Hahn and Pflug regarding the existence of proper holomorphic mappings between the Euclidean ball and the minimal ball, in a more general context.…”

“…In this paper our aim is to study this problem in the case of a special domain in C introduced by Hahn-Pflug [4] as the smallest norm in C n that extends the Euclidean norm in R n under certain restrictions. It has been studied in several recent works [7], [12], [9], [10], [11], [17]. The automorphism group of B ∞ is S 1 .O(n, R) (see [7]).…”