Remarks on the Kobayashi hyperbolicity of complex spaces
The hyperbolicity of Hartogs type domains has been studied for many years and many people obtained different results for some special cases. In the paper under review, the authors find the necessary and sufficient conditions for the hyperbolicity of Hartogs type domains in the general case and also find necessary and sufficient conditions for the tautness of the same domains. Furthermore, the authors generalize a result by \textit{Do Duc Thai, Pham Viet Duc}, and \textit{Tran Hue Minh} [Kyushu J. Math. 59, No.~2, 231--252 (2005; Zbl 1087.32011)], which is about hyperbolic imbeddedness. In the final part, the authors study the convergence of invariant functions and extend \textit{M. Kobayashi}'s result [Complex Variables, Theory Appl. 47, No.~2, 155--165 (2002; Zbl 1031.32015)] to some other cases.
scientific article; zbMATH DE number 5780194