Critical sets of proper holomorphic mappings

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 ${\mathbb{C}}^n$.

arXiv comment10 pages