Critical sets of proper holomorphic mappings

Sergey Pinchuk; Rasul Shafikov

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arXiv · 1402.0414

Critical sets of proper holomorphic mappings

Sergey Pinchuk·Rasul Shafikov

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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 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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Sergey Pinchuk, Rasul Shafikov. 2014-02-03. Critical sets of proper holomorphic mappings. https://arxiv.org/abs/1402.0414

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