Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 56, Number 4 (2004), 1087-1107.
On holomorphic mappings of complex manifolds with ball model
We consider holomorphic mappings of complex manifolds with ball model into complex manifolds which are quotients of bounded domains and estimate the dimension of the moduli space of holomorphic mappings in terms of the essential boundary dimension of target manifolds. For this purpose, we generalize a classical uniqueness theorem of Fatou-Riesz for bounded holomorphic functions on the unit disk to one for bounded holomorphic mappings on a bounded domain. This generalization enables us to establish rigidity and finiteness theorems for holomorphic mappings. We also discuss the rigidity for holomorphic mappings into quotients of some symmetric bounded domains. In the final section, we construct examples related to our results.
J. Math. Soc. Japan, Volume 56, Number 4 (2004), 1087-1107.
First available in Project Euclid: 27 September 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
Secondary: 32H20 30H35: BMO-spaces
SHIGA, Hiroshige. On holomorphic mappings of complex manifolds with ball model. J. Math. Soc. Japan 56 (2004), no. 4, 1087--1107. doi:10.2969/jmsj/1190905450. https://projecteuclid.org/euclid.jmsj/1190905450