# Holomorphic extension of meromorphic mappings along real analytic hypersurfaces

## TL;DR

This paper proves that under certain conditions, meromorphic mappings defined near a real analytic hypersurface can be extended holomorphically across the hypersurface, aiding the understanding of CR mappings between different-dimensional real hypersurfaces.

## Contribution

It establishes conditions under which meromorphic mappings extend holomorphically across real analytic hypersurfaces, advancing the theory of CR mappings and their regularity.

## Key findings

- Meromorphic mappings extend holomorphically under specific conditions.
- Extension results apply to strongly pseudoconvex algebraic hypersurfaces.
- The work facilitates analysis of CR mappings between hypersurfaces of different dimensions.

## Abstract

Let $M\subset \mathbb C^n$ be a real analytic hypersurface, $M'\subset \mathbb C^N$ $(N\geq n)$ 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.