## Germs of CR maps between real analytic hypersurfaces.(English)Zbl 0653.32020

Suppose H is a smooth CR mapping between two real-analytic hypersurfaces M and M’ in $${\mathbb{C}}^{n+1}$$ and let $$P_ 0\in M$$. The authors derive sufficient conditions for H to extend holomorphically to an ambient neighborhood of $$P_ 0$$. The conditions are given in terms of algebraic concepts, essential finiteness of M at $$P_ 0$$ and M’ at $$H(p_ 0)$$, and finite multiplicity of H at $$P_ 0$$. The techniques are rather algebraic as well, using such results as Nakayama’s Lemma, the Nullstellensatz, and the Weierstrass Preparation Theorem.
Reviewer: G.Harris

### MSC:

 32V40 Real submanifolds in complex manifolds
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### References:

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