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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Biholomorphic invariants of a hyperbolic manifold and some applications


Author: B. L. Fridman
Journal: Trans. Amer. Math. Soc. 276 (1983), 685-698
MSC: Primary 32H20; Secondary 32F15
MathSciNet review: 688970
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Abstract: A biholomorphically invariant real function $ {h_x}$ is defined for a hyperbolic manifold $ X$. Properties of such functions are studied. These properties are applied to prove the following theorem. If a hyperbolic manifold $ X$ can be exhausted by biholomorphic images of a strictly pseudoconvex domain $ D \subset {{\mathbf{C}}^n}$ with $ \partial D\; \in \;{C^3}$, then $ X$ is biholomorphically equivalent either to $ D$ or to the unit ball in $ {{\mathbf{C}}^n}$. The properties of $ {h_D}$ are also applied to some questions concerning the group of analytical automorphisms of a strictly pseudoconvex domain and to similar questions concerning polyhedra.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0688970-2
Article copyright: © Copyright 1983 American Mathematical Society