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Mathematics > Complex Variables

arXiv:1408.3306 (math)
[Submitted on 14 Aug 2014 (v1), last revised 5 Nov 2014 (this version, v2)]

Title:Rigidity of Proper Holomorphic Self-mappings of the Pentablock

Authors:Guicong Su, Zhenhan Tu, Lei Wang
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Abstract:The pentablock is a Hartogs domain over the symmetrized bidisc. The domain is a bounded inhomogeneous pseudoconvex domain, and does not have a $\mathcal{C}^{1}$ boundary. Recently, Agler-Lykova-Young constructed a special subgroup of the group of holomorphic automorphisms of the pentablock, and Kosiński completely described the group of holomorphic automorphisms of the pentablock. The purpose of this paper is to prove that any proper holomorphic self-mapping of the pentablock must be an automorphism.
Comments: 10 pages. To appear in Journal of Mathematical Analysis and Applications, arXiv admin note: text overlap with arXiv:1403.1960 and arXiv:1403.5214 by other authors
Subjects: Complex Variables (math.CV)
Cite as: arXiv:1408.3306 [math.CV]
  (or arXiv:1408.3306v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1408.3306
Journal reference: J. Math. Anal. Appl. 424(2015), 460-469
Related DOI: https://doi.org/10.1016/j.jmaa.2014.10.092

Submission history

From: Zhenhan Tu [view email]
[v1] Thu, 14 Aug 2014 14:51:05 UTC (10 KB)
[v2] Wed, 5 Nov 2014 12:45:11 UTC (10 KB)
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