Continuous proper holomorphic maps into bounded domains

Dor, Avner

doi:10.1090/S0002-9939-1993-1162088-9

Continuous proper holomorphic maps into bounded domains
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by Avner Dor PDF

Proc. Amer. Math. Soc. 119 (1993), 1145-1155 Request permission

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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