A criterion for biholomorphicity of self-mappings of generalized Fock-Bargmann-Hartogs domains

Abstract

By making use of our previous result on a localization principle for biholomorphic mappings between equidimensional Fock-Bargmann-Hartogs domains in ${ℂ}^n\times {ℂ}^m$ with $m\ge 2$ and the same technique as in our previous study of the Fock-Bargmann-Hartogs domains in ${ℂ}^n\times ℂ$, in this paper we establish a characterization of biholomorphicity of holomorphic self-mappings of generalized Fock-Bargmann-Hartogs domains. As a special case of this, we obtain the main result of a recent paper by Guo, Feng and Bi.