Geometry of quasi-circular domains and applications to tetrablock

Details Geometry of quasi-circular domains and applications to tetrablock Geometry of quasi-circular domains and applications to tetrablock

2009-08-22

arxiv.org/abs/0908.3249v2

Mathematics

Complex Variables

11 pages

Scientific paper

We prove that the Shilov boundary is invariant under proper holomorphic mappings between some classes of domains (containing among others quasi-balanced domains with the 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 $\mathbb C$-convex.

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