Automorphisms of the Hartogs Type Domains Over Classical Symmetric Domains

Abstract

In this paper we completely describe the automorphism group of the Hartogs type domains over bounded classical symmetric domains by using the ball characterization theorem about noncompact automorphism groups. As an application, we give plenty of examples of non-homogeneous domains in ℂn, for which the real dimension of the automorphism group is less than n2 - 1.

Rigidity of proper holomorphic mappings between certain unbounded non-hyperbolic domains

“…Step 2. We now prove that there exist ϕ * ∈ Aut(D n ′ ,m ′ (µ ′ )) such that ϕ * • ϕ −v • f has the desired form (1).…”

Techniques for Computations of the Automorphism Group of Domain

“…There is no result about smooth extension of biholomorphic maps. They proved that all boundary points except bΩ × {0} are strongly pseudoconvex in [1]. Using this fact, they prove that every automorphism preserves Ω × {0}.…”

Biholomorphisms between Hartogs domains over homogeneous Siegel domains

“…where || · || denotes the standard Hermitian norm on C N . The purpose of this paper is to prove the following two theorems: The motivation of this paper is to generalize the work of Ahn-Byun-Park in [1] and Tu-Wong in [13]. In their original work, Tu and Wang studied Hua domains over bounded symmetric domains of classical type and hence their result is more general.…”