The automorphism group of a certain unbounded non-hyperbolic domain

Abstract

In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain Dn,m in C n ×C m which is defined by the inequality ζ 2 < e −µ z 2 .

On the linearity of origin-preserving automorphisms of quasi-circular domains in Cn

“…Indeed, it is observed in our previous paper [7] that Theorem 1.1 remains true for any circular domains whenever "the Bergman mapping" is well-defined. Although it is a simple observation from Ishi-Kai's paper [4], it appears not to have been noticed by many mathematicians.…”

“…• an explicit description of the automorphism group of D n,m [7], • rigidity properties of proper holomorphic mappings for D n,m [13].…”

“…Let us consider the weights (m 1 , m 2 , m 3 ) = (3, 5, 7),(4,5,7). For these weights, we can easily check the conditions (a), (b').…”

“…If (m 1 , m 2 , m 3 ) =(3,7,11), the set I 2 m,2 is given byI 2 m,2 = {12,13, 14, 15, 16, 17, 18, 19}. Thus this weight satisfies the conditions (a), (b) with N = 2.…”

Rigidity of proper holomorphic mappings between generalized Fock–Bargmann–Hartogs domains

“…The above conditions are obviously satisfied by the bounded domain. Kim-Ninh-Yamamori [13] proved the following result.…”