Abstract
Answering all questions—concerning proper holomorphic mappings between generalized Hartogs triangles—posed by Jarnicki and Plfug (First steps in several complex variables: Reinhardt domains, EMS Textbooks in Mathematics, European Mathematical Society Publishing House, 2008), we characterize the existence of proper holomorphic mappings between generalized Hartogs triangles and give their explicit form. In particular, we completely describe the group of holomorphic automorphisms of such domains and establish rigidity of proper holomorphic self-mappings on them. Moreover, we also complete the classification of proper holomorphic mappings in the class of complex ellipsoids which was initiated by Landucci and continued by Dini and Selvaggi Primicerio.
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