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Let M be a generic CR submanifold in ${ℂ}^{m+n}$, m = CR dim M ≥ 1, n = codim M ≥ 1, d = dim M = 2m + n. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple $(f{,}_f,\left[{\Gamma }_f\right])$, where: 1) $f{:}_f\to Y$ is a ¹-smooth mapping defined over a dense open subset ${}_f$ of M with values in a projective manifold Y; 2) the closure ${\Gamma }_f$ of its graph in ${ℂ}^{m+n}\times Y$ defines an oriented scarred ¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) $d\left[{\Gamma }_f\right]=0$ in the sense of currents. We prove that $(f{,}_f,\left[{\Gamma }_f\right])$ extends meromorphically to a wedge...

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’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...