An application of a Diederich–Ohsawa theorem in characterizing some Hartogs domains

Abstract

Abstract. Applying a theorem due to Diederich and Ohsawa on weighted Bergman kernels, we characterize some Hartogs domains by their holomorphic automorphisms.

The holomorphic automorphism groups of twisted Fock-Bargmann-Hartogs domains

“…This is generalized by the second author in [25] for general m and n. By using an explicit form of Bergman kernel, the automorphism group of Ω FBH is determined in [9] by the authors of the present paper and Ninh. For other works related to these domains, see [2], [10], [11], [14], [22], [30] and references therein.…”

Balanced metrics on the Fock–Bargmann–Hartogs domains

“…The Cartan-Hartogs domains and the Fock-Bargmann-Hartogs domains are two kinds of typical Hartogs domains (e.g., see Kim-Yamamori [14]). The Cartan-Hartogs domains are some Hartogs domains over bounded symmetric domains and there are many researches about the balanced metrics on the Cartan-Hartogs domains (e.g., see Feng-Tu [11,12], Loi-Zedda [19] and Zedda [25]).…”