UNIQUE JET DETERMINATION AND EXTENSION OF GERMS OF CR MAPS INTO SPHERES Academic Article

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