Critical sets of proper holomorphic mappings

Pinchuk, Sergey; Shafikov, Rasul

doi:10.1090/proc/12529

Critical sets of proper holomorphic mappings
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by Sergey Pinchuk and Rasul Shafikov PDF

Proc. Amer. Math. Soc. 143 (2015), 4335-4345 Request permission

Abstract:

It is shown that if a proper holomorphic map $f: \mathbb C^n \to \mathbb C^N$, $1<n\le N$, sends a pseudoconvex real analytic hypersurface $M$ of finite type into another such hypersurface, then any $(n-1)$-dimensional component of the critical locus of $f$ intersects both sides of $M$. We apply this result to the problem of boundary regularity of proper holomorphic mappings between bounded domains in $\mathbb C^n$.

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