## Illinois Journal of Mathematics

### Condition R and holomorphic mappings of domains with generic corners

#### Abstract

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.

#### Article information

Source
Illinois J. Math., Volume 57, Number 4 (2013), 1035-1055.

Dates
First available in Project Euclid: 1 December 2014

https://projecteuclid.org/euclid.ijm/1417442562

Digital Object Identifier
doi:10.1215/ijm/1417442562

Mathematical Reviews number (MathSciNet)
MR3285867

Zentralblatt MATH identifier
1307.32015

Subjects
Primary: 32H40: Boundary regularity of mappings

#### Citation

Chakrabarti, Debraj; Verma, Kaushal. Condition R and holomorphic mappings of domains with generic corners. Illinois J. Math. 57 (2013), no. 4, 1035--1055. doi:10.1215/ijm/1417442562. https://projecteuclid.org/euclid.ijm/1417442562

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