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

2020/08/17 by Mir, Nordine, Zaitsev, Dmitri · 1 citation
#32D15 #32H02 #32H04 #32H12 #32V20 #32V25 #32V40 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2008.07194

Abstract

We provide a new way of simultaneously parametrizing arbitrary local CR maps from real-analytic generic manifolds M⊂ \mathbb C^N into spheres \mathbb S^2N'-1⊂ \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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