# One side continuity of meromorphic mappings between real analytic hypersurfaces

## TL;DR

The paper proves that certain meromorphic mappings from real analytic hypersurfaces in complex space are continuous from the concave side, leading to results on their analytic continuation along CR-paths.

## Contribution

It establishes the continuity of meromorphic mappings from strictly pseudoconvex hypersurfaces to compact sets without complex curves, and extends analytic continuation results in complex analysis.

## Key findings

- Continuity of meromorphic mappings from the concave side of hypersurfaces.
- Analytic continuation along CR-paths for mappings to spherical hypersurfaces.
- Extension of previous results to all dimensions.

## Abstract

We prove that a meromorphic mapping, which sends a peace of a real analytic strictly pseudoconvex hypersurface in $\cc^2$ to a compact subset of $\cc^N$ which doesn't contain germs of non-constant complex curves is continuous from the concave side of the hypersurface. This implies the analytic continuability along CR-paths of germs of holomorphic mappings from real analytic hypersurfaces with non-vanishing Levi form to the locally spherical ones in all dimensions.