Condition R and holomorphic mappings of domains with generic corners

Debraj Chakrabarti; Kaushal Verma

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arXiv · 1209.0325

Condition R and holomorphic mappings of domains with generic corners

Debraj Chakrabarti·Kaushal Verma

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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.

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BibTeX RIS

Debraj Chakrabarti, Kaushal Verma. 2014-02-22. Condition R and holomorphic mappings of domains with generic corners. https://arxiv.org/abs/1209.0325

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