Geometry of quasi-circular domains and applications to tetrablock
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Abstract:
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 $\mathbb C$-convex.
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Additional Information
- Łukasz Kosiński
- Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Łojasiewicza 6, 30-348 Kraków, Poland
- MR Author ID: 825007
- Email: lukasz.kosinski@im.uj.edu.pl
- Received by editor(s): November 11, 2009
- Received by editor(s) in revised form: November 12, 2009, and March 10, 2010
- Published electronically: July 16, 2010
- Additional Notes: This work was partially supported by the Research Grant of the Polish Ministry of Science and Higher Education N$^{\text o}$ N N201 271435.
- Communicated by: Franc Forstneric
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 559-569
- MSC (2010): Primary 32H35, 32A07
- DOI: https://doi.org/10.1090/S0002-9939-2010-10493-8
- MathSciNet review: 2736338