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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

66
66

Jul 20, 2013
07/13

by
J. Merker; Egmont Porten

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Soient $M$ une vari\'et\'e CR localement plongeable et $\Phi\subset M$ un ferm\'e. On donne des conditions suffisantes pour que les fonctions $L_{loc}^1$ qui sont CR sur $M\backslash \Phi$ le soient aussi sur $M$ tout entier.

Source: http://arxiv.org/abs/math/9902039v1

90
90

Jul 20, 2013
07/13

by
J. Merker; Egmont Porten

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We endeavour a systematic approach for the removal of singularities for CR functions on an arbitrary embeddable CR manifold.

Source: http://arxiv.org/abs/math/9902040v1

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42

Jul 20, 2013
07/13

by
J. Merker; Egmont Porten

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Let $M$ be a generic CR submanifold in $\C^{m+n}$, $m= CRdim M \geq 1$,$n=codim M \geq 1$, $d=dim M = 2m+n$. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple $(f,{\cal D}_f, [\Gamma_f])$, where: 1. $f: {\cal D}_f \to Y$ is a ${\cal C}^1$-smooth mapping defined over a dense open subset ${\cal D}_f$ of $M$ with values in a projective manifold $Y$; 2. The closure $\Gamma_f$ of its graph in $\C^{m+n} \times Y$ defines a oriented scarred ${\cal C}^1$-smooth CR manifold of CR...

Source: http://arxiv.org/abs/math/9902038v1

51
51

Sep 23, 2013
09/13

by
C. Denson Hill; Egmont Porten

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The H-principle, which is the analogue, for CR manifolds, of the classical Hartogs principle in several complex variables, is known to be valid in the small on a pseudoconcave CR manifold of any codimension. However it fails in the large, as has been shown by the counterexample found in [HN1]. Hence there is an underlying obstruction to the global H-principle on a pseudoconcave CR manifold. The purpose of this note is to take the first steps toward a deeper understanding of this obstruction.

Source: http://arxiv.org/abs/0710.5728v1