Journal of the Mathematical Society of Japan

On holomorphic mappings of complex manifolds with ball model

Hiroshige SHIGA

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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 C2 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

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

First available in Project Euclid: 27 September 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

complex hyperbolic geometry Fatou-Riesz theorem rigidity of holomorphic mappings


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.

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