Geometry of quasi-circular domains and applications to tetrablock - Mathematics > Complex VariablesReport as inadecuate




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Abstract: We prove that the Shilov boundary is invariant under proper holomorphicmappings between some classes of domains containing among othersquasi-balanced domains with the continuous Minkowski functionals. Moreover, weobtain an extension theorem for proper holomorphic mappings betweenquasi-circular domains.Using these results we show that there are no non-trivial proper holomorphicself-mappings in the tetrablock. Another important result of our work is adescription of Shilov boundaries of a large class of domains containing amongother the symmetrized polydisc and the tetrablock.It is also shown that the tetrablock is not $\mathbb C$-convex.



Author: Lukasz Kosinski

Source: https://arxiv.org/



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