Boundary regularity of correspondences in $\pmb{{\mbf C}^n}$

Rasul Shafikov; Kaushal Verma

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Boundary regularity of correspondences in $\pmb{{\mbf C}^n}$

Rasul Shafikov·Kaushal Verma

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Abstract

Let $M, M'$ be smooth, real analytic hypersurfaces of finite type in ${\mbf C^n}$ and $\h f$ a holomorphic correspondence (not necessarily proper) that is defined on one side of $M$, extends continuously up to $M$ and maps $M$ to $M'$. It is shown that $\h f$ must extend across $M$ as a locally proper holomorphic correspondence. This is a version for correspondences of the Diederich--Pinchuk extension result for CR maps.

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BibTeX RIS

Rasul Shafikov, Kaushal Verma. 2006-07-24. Boundary regularity of correspondences in $\pmb{{\mbf C}^n}$. https://arxiv.org/abs/math/0607594

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