Holomorphic extension of meromorphic mappings along real analytic hypersurfaces

Abstract

Let $M\subset {\mathbb{C}}^n$ be a real analytic hypersurface, $M^{\prime }\subset {\mathbb{C}}^N$ $(N\ge n)$ be a strongly pseudoconvex real algebraic hypersurface of the special form and $F$ be a meromorphic mapping in a neighborhood of a point $p\in M$ which is holomorphic in one side of $M$. Assuming some additional conditions for the mapping $F$ on the hypersurface $M$, we proved that $F$ has a holomorphic extension to $p$. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensions.

Statement of Theorem 1.1 was corrected and some typos were fixed upon the referee's comments