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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Embedding strictly pseudoconvex domains into balls


Author: Franc Forstnerič
Journal: Trans. Amer. Math. Soc. 295 (1986), 347-368
MSC: Primary 32H99; Secondary 32F15, 32F25
MathSciNet review: 831203
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Abstract: Every relatively compact strictly pseudoconvex domain $ D$ with $ {{\mathbf{C}}^2}$ boundary in a Stein manifold can be embedded as a closed complex submanifold of a finite dimensional ball. However, for each $ n \geq 2$ there exist bounded strictly pseudoconvex domains $ D$ in $ {\mathbb{C}^n}$ with real-analytic boundary such that no proper holomorphic map from $ D$ into any finite dimensional ball extends smoothly to $ \overline D $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0831203-7
PII: S 0002-9947(1986)0831203-7
Article copyright: © Copyright 1986 American Mathematical Society