pith. sign in

arxiv: 1107.3374 · v2 · pith:VIUQTDRRnew · submitted 2011-07-18 · 🧮 math.CV · math.AP

mathcal{C}^(infty)-hypoellipticity and extension of CR functions

classification 🧮 math.CV math.AP
keywords extensionhypoellipticityfunctionsholomorphicambientapplicationarticleclass
0
0 comments X
read the original 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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.