Related papers: Analyticit\'e des applications CR dans des vari\'e…
Iterated Segre mappings of real analytic generic submanifolds in complex space have been an essential tool in the study of holomorphic, formal, and CR mappings between such manifolds. In this paper we present a theory of iterated Segre…
The following theorem is proved: Let M be a locally Lipschitz hypersurface in C^n with one-sided extension property at each point (e.g., without analytic discs). Let S be a closed subset of M and f : M \ S ---> C^m \ E is a CR-mapping of…
This paper provides a connection between two distinct branches of research in CR geometry -- namely, analytic and geometric conditions that suffice to establish the closed range of the Cauchy-Riemann operator and CR invariants on CR…
Several questions in CR geometry lead naturally to the study of bihomogeneous polynomials $r(z,\bar{z})$ on $\C^n \times \C^n$ for which $r(z,\bar{z})\norm{z}^{2d}=\norm{h(z)}^2$ for some natural number $d$ and a holomorphic polynomial…
We approximate smooth maps defined on non-compact totally real manifolds by holomorphic automorphisms of $\mathbb C^n$.
We describe complex conjugation on the primitive middle-dimensional algebraic de Rham cohomology of a smooth projective hypersurface defined over a number field that admits a real embedding. We use Griffiths' description of the cohomology…
We study, in some models of Levi flat CR manifolds, the correspondence between the tangential Cauchy-Riemann complex and the complex defined by the associated real foliation.
In this article the notion of ultradifferentiable CR manifold is introduced and an ultradifferentiable regularity result for finitely nondegenerate CR mappings is proven. Here ultradifferentiable means with respect to Denjoy-Carleman…
This is an extensive (published) survey on CR geometry, whose major themes are: formal analytic reflection principle; generic properties of Systems of (CR) vector fields; pairs of foliations and conjugate reflection identities; Sussmann's…
Although the concept of defect of an analytic disc attached to a generic manifold of $\C^{n}$ seems to play a merely technical role, it turns out to be a rather deep and fruitful notion for the extendability of CR functions defined on the…
We analyze the differential relation corresponding to integrability of almost complex structures, reformulated as a directed immersion relation by Demailly and Gaussier. Combining results of Clemente [3], we show that applying h-principle…
Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We show how to systematically…
In this paper, we consider local holomorphic mappings f: M\to M' between real algebraic CR generic manifolds (or more generally, real algebraic sets with singularities) in the complex euclidean spaces of different dimensions and we search…
Given a finite collection of $C^1$ vector fields on a $C^2$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields are real analytic. We give…
Totally real surfaces in the nearly K\"ahler $\mathbb{C}P^3$ are investigated and are completely classified under various additional assumptions, resulting in multiple new examples. Among others, the classification includes totally real…
Let V be a real hypersurface of class C^k, k>=3, in a complex manifold M of complex dimension n+1, HT(V) the holomorphic tangent bundle to V giving the induced CR structure on V. Let \theta be a contact form for (V,HT(V)), \xi_0 the Reeb…
We study deformations of holomorphic maps of compact, complex, K\"ahler manifolds. In particular, we describe a generalization of Bloch's semiregularity map that annihilates obstructions to deform holomorphic maps with fixed codomain.
We study the equivalence problem under projective transformation for CR-hypersurfaces of complex projective space. A complete set of projective differential invariants for analytic hypersurfaces is given. The self-dual strongly C-linearly…
We develop the notion of renormalized energy in CR geometry, for maps from a strictly pseudoconvex pseudohermitian manifold to a Riemannian manifold. This energy is a CR invariant functional, whose critical points, which we call CR-harmonic…
We extend the Newlander-Nirenberg theorem to manifolds with almost complex structures that have somewhat less than Lipschitz regularity. We also discuss the regularity of local holomorphic coordinates in the integrable case, with particular…