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Critical sets of proper holomorphic mappings


Authors: Sergey Pinchuk and Rasul Shafikov
Journal: Proc. Amer. Math. Soc. 143 (2015), 4335-4345
MSC (2010): Primary 32D15, 32V40, 32H02, 32H04, 32H35, 32M99, 32T25, 34M35
Published electronically: June 18, 2015
MathSciNet review: 3373932
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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 $ 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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Additional Information

Sergey Pinchuk
Affiliation: Department of Mathematics, Rawles Hall, Indiana University, 831 East 3rd Street, Bloomington, Indiana 47405
Email: pinchuk@indiana.edu

Rasul Shafikov
Affiliation: Department of Mathematics, The University of Western Ontario, London, Ontario N6A 5B7 Canada
Email: shafikov@uwo.ca

DOI: https://doi.org/10.1090/proc/12529
Keywords: Holomorphic mappings, holomorphic correspondences, real hypersurfaces, Segre varieties, boundary regularity, analytic continuation
Received by editor(s): February 3, 2014
Received by editor(s) in revised form: April 17, 2014, and April 24, 2014
Published electronically: June 18, 2015
Communicated by: Franc Forstneric
Article copyright: © Copyright 2015 American Mathematical Society