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

TL;DR

This paper introduces a new parametrization method for local CR maps into spheres, leading to results on their unique jet determination and global extension, advancing understanding of CR geometry.

Contribution

It presents a novel parametrization technique for local CR maps into spheres, enabling new rigidity results and extension theorems in CR geometry.

Findings

Achieved a universal rational parametrization of CR maps

Proved unique jet determination for local CR maps

Established conditions for global extension of CR maps

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 ${\mathbb S}^{2N'-1}\subset {\mathbb C}^{N'}$ of any dimension. The parametrization is obtained as a composition of universal rational maps with a holomorphic map depending only on $M$. As applications, we obtain rigidity results of different flavours such as unique jet determination and global extension of local CR maps.