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 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