Rigidity of proper holomorphic maps between nonequidimensional Fock–Bargmann–Hartogs domains

Abstract In this article, we introduce a novel rigidity theorem that investigates proper holomorphic maps between Fock–Bargmann–Hartogs domains of varying dimensions. Unlike previous studies, this theorem does not impose any restrictions on the codimension. Our main result demonstrates that any such proper holomorphic map can be equivalently represented as , where is a positive integer.