Critical sets of proper holomorphic mappings

2014/02/03 by Sergey Pinchuk, Pinchuk, Sergey, Rasul Shafikov +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1402.0414

10 pages

arxiv created 2014/02/03 · arxiv updated 2014/02/04

Abstract

It is shown that if a proper holomorphic map f: \mathbb Cⁿ → \mathbb C^N, 1<n≤ 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 Cⁿ.

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