Open Access
Winter 2013 Condition R and holomorphic mappings of domains with generic corners
Debraj Chakrabarti, Kaushal Verma
Illinois J. Math. 57(4): 1035-1055 (Winter 2013). DOI: 10.1215/ijm/1417442562


A piecewise smooth domain is said to have generic corners if the corners are generic CR manifolds. It is shown that a biholomorphic mapping from a piecewise smooth pseudoconvex domain with generic corners in complex Euclidean space that satisfies Condition R to another domain extends as a smooth diffeomorphism of the respective closures if and only if the target domain is also piecewise smooth with generic corners and satisfies Condition R. Further it is shown that a proper map from a domain with generic corners satisfying Condition R to a product domain of the same dimension extends continuously to the closure of the source domain in such a way that the extension is smooth on the smooth part of the boundary. In particular, the existence of such a proper mapping forces the smooth part of the boundary of the source to be Levi degenerate.


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Debraj Chakrabarti. Kaushal Verma. "Condition R and holomorphic mappings of domains with generic corners." Illinois J. Math. 57 (4) 1035 - 1055, Winter 2013.


Published: Winter 2013
First available in Project Euclid: 1 December 2014

zbMATH: 1307.32015
MathSciNet: MR3285867
Digital Object Identifier: 10.1215/ijm/1417442562

Primary: 32H40

Rights: Copyright © 2013 University of Illinois at Urbana-Champaign

Vol.57 • No. 4 • Winter 2013
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