Unique jet determination and extension of germs of CR maps into spheres
Unique jet determination and extension of germs of CR maps into spheres
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DOI：
10.1090/tran/8280
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发表时间：
2020-08
影响因子：
1.3
通讯作者：
N. Mir;D. Zaitsev
中科院分区：
文献类型：
--
作者：
N. Mir;D. Zaitsev
我们提供了一种新的方法来同时将实解析一般流形$M\子集{\mathbb C}^N$中的任意局部CR映射参数化为任意维球面${\mathbb S}^{2N‘-1}\子集{\mathbb C}^{N’}$.该参数化为泛有理映射与仅依赖于$M$的全纯映射的组合。作为应用，我们得到了不同口味的刚性结果，如唯一喷流判定和局部CR图的全局扩展。
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.