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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the volumes of images of holomorphic mappings in $ {\bf C}\sp n$


Author: H. Alexander
Journal: Proc. Amer. Math. Soc. 98 (1986), 461-466
MSC: Primary 32H35; Secondary 31B20, 32E25
MathSciNet review: 857941
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Abstract: Let $ f$ be a holomorphic map from the unit ball in complex $ n$-space to complex $ n$-space. We establish a lower bound for the volume, taken without multiplicity, of the image of $ f$. The estimate is in terms of the boundary values of $ f$. This generalizes some known results in one complex variable. The proof uses the methods of uniform algebras.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0857941-3
PII: S 0002-9939(1986)0857941-3
Article copyright: © Copyright 1986 American Mathematical Society