## Journal of the Mathematical Society of Japan

### On holomorphic mappings of complex manifolds with ball model

Hiroshige SHIGA

#### Abstract

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 $C^{2}$ 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.

#### Article information

Source
J. Math. Soc. Japan, Volume 56, Number 4 (2004), 1087-1107.

Dates
First available in Project Euclid: 27 September 2007

https://projecteuclid.org/euclid.jmsj/1190905450

Digital Object Identifier
doi:10.2969/jmsj/1190905450

Mathematical Reviews number (MathSciNet)
MR2091418

Zentralblatt MATH identifier
1066.32022

Subjects
Primary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
Secondary: 32H20 30H35: BMO-spaces

#### Citation

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