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

Mir, Nordine; Zaitsev, Dmitri

doi:10.1090/tran/8280

Unique jet determination and extension of germs of CR maps into spheres
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Trans. Amer. Math. Soc. 374 (2021), 2149-2166 Request permission

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.

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