Unique jet determination and extension of germs of CR maps into spheres

Abstract

We provide a new way of simultaneously parametrizing arbitrary local CR maps from real-analytic generic manifolds $M\subset {\mathbb{C}}^N$ into spheres ${\mathbb{S}}^{2N^{\prime }-1}\subset {\mathbb{C}}^{N^{\prime }}$ of any dimension. The parametrization is obtained as a composition of universal rational maps with a holomorphic map depending only on $M$. As applications, we obtain rigidity results of different flavours such as unique jet determination and global extension of local CR maps.