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.

中文翻译：

---

独特的射流测定和将 CR 图的细菌扩展到球体中

我们提供了一种将任意局部 CR 映射从实解析通用流形 $M\subset {\mathbb C}^N$ 同时参数化为球体 ${\mathbb S}^{2N'-1}\subset {\mathbb C}^{N'}$ 的任何维度。参数化是作为通用有理映射与仅依赖于 $M$ 的全纯映射的组合获得的。作为应用，我们获得了不同风格的刚性结果，例如独特的喷射确定和局部 CR 地图的全局扩展。