70
70
Jul 20, 2013
07/13
by
Mauro Nacinovich; Egmont Porten
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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.
Source: http://arxiv.org/abs/1107.3374v2
64
64
Jul 22, 2013
07/13
by
Andrea Altomani; C. Denson Hill; Mauro Nacinovich; Egmont Porten
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We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for $CR$ manifolds and H\"ormander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which the distribution of $(0,1)$ vector fields satisfies a subelliptic estimate. v2:...
Source: http://arxiv.org/abs/0807.4857v2
40
40
Sep 18, 2013
09/13
by
Mauro Nacinovich; Egmont Porten
texts
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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.
Source: http://arxiv.org/abs/1201.1704v1
3
3.0
Jun 29, 2018
06/18
by
Mauro Nacinovich; Egmont Porten
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We introduce various notions of q-pseudo-concavity for abstract CR manifolds and we apply these notions to the study of hyoo-ellipticity, maximum modulus principle and Cauchy problems for CR functions.
Topics: Complex Variables, Mathematics
Source: http://arxiv.org/abs/1611.02553
