Geometry of quasi-circular domains and applications to tetrablock

• Autores: Lukasz Kosinski
• Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 139, Nº 2, 2011, págs. 559-569
• Idioma: inglés
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• Resumen

  • We prove that the Shilov boundary is invariant under proper holomorphic mappings between some classes of domains (containing among others quasi-balanced domains with continuous Minkowski functionals). Moreover, we obtain an extension theorem for proper holomorphic mappings between quasi-circular domains.

    Using these results we show that there are no non-trivial proper holomorphic self-mappings in the tetrablock. Another important result of our work is a description of Shilov boundaries of a large class of domains (containing among other the symmetrized polydisc and the tetrablock).

    It is also shown that the tetrablock is not -convex.