Analyticity of smooth CR mappings of generic submanifolds

Details Analyticity of smooth CR mappings of generic submanifolds Analyticity of smooth CR mappings of generic submanifolds

2006-08-10

arxiv.org/abs/math/0608272v1

Mathematics

Complex Variables

16 pages

Scientific paper

We consider a smooth CR mapping $f$ from a real-analytic generic submanifold $M$ in $\bC^N$ into $\bC^N$. For $M$ of finite type and essentially finite at a point $p\in M$, and $f$ formally finite at $p$, we give a necessary and sufficient condition for $f$ to extend as a holomorphic mapping in some neighborhood of $p$. In a similar vein, we consider a formal holomorphic mapping $H$ and give a necessary and sufficient condition for $H$ to be convergent.

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