$\mathcal{C}^{\infty}$-hypoellipticity and extension of $CR$ functions

Mauro Nacinovich; Egmont Porten

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arXiv · 1107.3374

$\mathcal{C}^{\infty}$-hypoellipticity and extension of $CR$ functions

Mauro Nacinovich·Egmont Porten

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Abstract

Let $M$ be a $CR$ submanifold of a complex manifold $X$. The main result of this article is to show that $CR$-hypoellipticity at $p_0\in{M}$ is necessary and sufficient for holomorphic extension of all germs of $CR$ functions to an ambient neighborhood in $X$. As an application, we obtain that $CR$-hypoellipticity implies the existence of generic embeddings and prove holomorphic extension for a large class of $CR$ manifolds satisfying a higher order Levi pseudoconcavity condition.

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Mauro Nacinovich, Egmont Porten. 2011-11-07. $\mathcal{C}^{\infty}$-hypoellipticity and extension of $CR$ functions. https://arxiv.org/abs/1107.3374

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