Related papers: Real-analytic coordinates for smooth strictly pseu…

In this paper we prove that a dynamically convex starshaped hypersurface in $\mathbb{C}^2$ which is invariant under complex conjugation admits a global surface of section which is invariant under conjugation as well. We obtain this…

Let $M$ be a pseudoconvex, oriented, bounded and closed CR submanifold of $\mathbb{C}^{n}$ of hypersurface type. Our main result says that when a certain $1$-form on $M$ is exact on the null space of the Levi form, then the complex Green…

We define a new local invariant (called degeneracy) associated to a triple (M,M',H), where M and M' are real submanifolds of C^N and C^N', respectively, and H: M->M' is either a holomorphic map, a formal holomorphic map, or a smooth CR-map.…

We introduce new biholomorphic invariants for real-analytic hypersurfaces in 2-dimensional complex space and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms of the new…

Let $\Omega$ be a smooth real analytic submanifold of a complex manifold $X$. We establish and study the link between the following 3 subjects: 1) topological properties of smooth families of attached analytic discs, the manifold $\Omega$…

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these…

We prove that if two real-analytic hypersurfaces in $\mathbb C^2$ are equivalent formally, then they are also $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic…

In this paper, we examine holomorphic Segre preserving maps between the complexifications of real hypersurfaces in $\mathbb{C}^{n+1}$. In particular, we find several sufficient conditions ensuring that Segre transversality and total Segre…

The main result of this paper is that the identity component of the automorphism group of a compact, connected, strictly pseudoconvex CR manifold is compact unless the manifold is CR equivalent to the standard sphere. In dimensions greater…

We compute a recently introduced geometric invariant of stricly pseudoconvex CR 3-manifolds for certain circle invariant spherical CR structures on Seifert manifolds. We give applications to the problem of filling the CR manifold by a…

One constructs an example of a generic quadratic submanifold of codimension $5$ in $\Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $3.$

Let $\Omega \subset {\mathbb C}^n \times {\mathbb R}$ be a bounded domain with smooth boundary such that $\partial \Omega$ has only nondegenerate elliptic CR singularities, and let $f \colon \partial \Omega \to {\mathbb C}$ be a smooth…

We study a germ of real analytic n-dimensional submanifold of $C^n$ that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the maximum number of deck transformations,…

In this paper, we investigate analytic and geometric properties of obstruction flatness of strongly pseudoconvex CR hypersurfaces of dimension $2n-1$. Our first two results concern local aspects. Theorem 3.2 asserts that any strongly…

CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation into a normal form. The quadratic…

This paper deals with the notion of quadratic differential in spherical CR geometry (or more generally on strictly pseudoconvex CR manifolds). We get to this notion by studying a splitting of Rumin complex and discuss its first features…

Let M be a real analytic strictly pseudoconvex manifold of higher codimension in complex space, and let M' be the cartesian product of two or more compact real analytic strictly convex hypersurfaces. We prove that a germ of a biholomorphic…

We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kaehler manifolds with compact strongly pseudoconvex…

We investigate the $p$-essential normality of Hilbert quotient submodules on a relatively compact smooth strongly pseudoconvex domain in a complex manifold satisfying Property (S). For analytic subvarieties that have compact singularities…

We first construct a counterexample of a generic quadratic submanifold of codimension $5$ in $\Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $4.$ This example also…