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 ⊂ C N M\subset \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.