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Continuous Proper Holomorphic Maps into Bounded Domains

Avner Dor
Proceedings of the American Mathematical Society
Vol. 119, No. 4 (Dec., 1993), pp. 1145-1155
DOI: 10.2307/2159977
Stable URL: http://www.jstor.org/stable/2159977
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Continuous Proper Holomorphic Maps into Bounded Domains
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Abstract

A continuous proper holomorphic map is constructed from the unit ball of CN to a smooth bounded domain in CM (2 ≤ N ≤ 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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