On the hull of holomorphy of an -manifold in
On the Kuranishi family of deformations of complex structures over a tubular neighborhood of a strongly pseudo convex boundary with complex dimension 3.
On the local meromorphic extension of CR meromorphic mappings
Let M be a generic CR submanifold in , 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 , where: 1) is a ¹-smooth mapping defined over a dense open subset of M with values in a projective manifold Y; 2) the closure of its graph in defines an oriented scarred ¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) in the sense of currents. We prove that extends meromorphically to a wedge...
On the local solution of the tangential Cauchy-Riemann equations
On the Nature of Thin Complements of Complete Kähler Metrics.
On the nonexistence of CR functions on Levi-flat CR manifolds.
We show that no compact Levi-flat CR manifold of CR codimension one admits a continuous CR function which is nonconstant along leaves of the Levi foliation. We also prove the nonexistence of certain CR functions on a neighborhood of a compact leaf of some Levi-flat CR 3-manifolds, and apply it to showing that some foliated 3-manifolds cannot be embedded as smooth Levi-flat real hypersurfaces in complex surfaces.
On the partial algebraicity of holomorphic mappings between two real algebraic sets
The rigidity properties of the local invariants of real algebraic Cauchy-Riemann structures imposes upon holomorphic mappings some global rational properties (Poincaré 1907) or more generally algebraic ones (Webster 1977). Our principal goal will be to unify the classical or recent results in the subject, building on a study of the transcendence degree, to discuss also the usual assumption of minimality in the sense of Tumanov, in arbitrary dimension, without rank assumption and for holomorphic...
On the Polynomial Convexity of the Union ot Two Maximal Totally Real Subspaces of Cn.
On the proof of Kuranishi's embedding theorem
On the real analytic Levi flat hypersurfaces in complex tori of dimension two
We compute the Levi form of the logarithm of the distance function for real hypersurfaces in two dimensional complex tori, and discuss the characterization of Levi flat hypersurfaces there.
On the regularity of CR structures for almost CR vector bundles.
On the smoothness of Levi-foliations.
We study the regularity of the induced foliation of a Levi-flat hypersurface in Cn, showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question.
On the space of the analytic discs which are transversal to a smooth real hypersurface of
On totally real submanifolds in a nearly Kähler manifold.