English

Rigidity of Proper Holomorphic Self-mappings of the Pentablock

Complex Variables 2014-12-15 v2

Abstract

The pentablock is a Hartogs domain over the symmetrized bidisc. The domain is a bounded inhomogeneous pseudoconvex domain, and does not have a C1\mathcal{C}^{1} boundary. Recently, Agler-Lykova-Young constructed a special subgroup of the group of holomorphic automorphisms of the pentablock, and Kosi\'nski 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.

Keywords

Cite

@article{arxiv.1408.3306,
  title  = {Rigidity of Proper Holomorphic Self-mappings of the Pentablock},
  author = {Guicong Su and Zhenhan Tu and Lei Wang},
  journal= {arXiv preprint arXiv:1408.3306},
  year   = {2014}
}

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