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

 

Continuous proper holomorphic maps into bounded domains


Author: Avner Dor
Journal: Proc. Amer. Math. Soc. 119 (1993), 1145-1155
MSC: Primary 32H35; Secondary 32H02
MathSciNet review: 1162088
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Abstract: A continuous proper holomorphic map is constructed from the unit ball of $ {\mathbb{C}^N}$ to a smooth bounded domain in $ {\mathbb{C}^M}(2 \leqslant N \leqslant M - 1)$. The construction is done at a strongly convex corner of the target domain. At each stage the map is pushed farther into the boundary in a direction almost tangent to the boundary at a close vicinity. The close point property is employed, along with suitable peak functions, to obtain a minimal codimension. It appears to be close to the most general construction that can be made by summation of peak functions.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1162088-9
PII: S 0002-9939(1993)1162088-9
Article copyright: © Copyright 1993 American Mathematical Society