Related papers: Extension of CR-functions on wedges

Let $M$ be a smooth compact $CR$ manifold of $CR$ dimension $n$ and $CR$ codimension $k$, which has a certain local extension property $E$. In particular, if $M$ is pseudoconcave, it has property $E$. Then the field $\Cal K(M)$ of $CR$…

Let g be an integer greater than 1. A uniform version of the Parshin-Arakelov theorem on the finiteness of the set of non-isotrivial curves of genus g over a function field, with fixed degeneracy locus, is proved. This is applied to obtain…

Let $M \subset {\mathbb{C}}^{n+1}$, $n \geq 2$, be a real codimension two CR singular real-analytic submanifold that is nondegenerate and holomorphically flat. We prove that every real-analytic function on $M$ that is CR outside the CR…

We consider canonical fibrations and algebraic geometric structures on homogeneous CR manifolds, in connection with the notion of CR algebra. We give applications to the classifications of left invariant CR structures on semisimple Lie…

A CR manifold $M$, with CR distribution $\mathcal D^{10}\subset T^\mathbb C M$, is called {\it totally nondegenerate of depth $\mu$} if: (a) the complex tangent space $T^\mathbb C M$ is generated by all complex vector fields that might be…

We prove the following variant of Levi's Enlargement Lemma: for an arbitrary arrangement $\mathcal{A}$ of $x$-monotone pseudosegments in the plane and a pair of points $a,b$ with distinct $x$-coordinates and not on the same pseudosegment,…

Degenerations of Lie algebras of meromorphic vector fields on elliptic curves (i.e. complex tori) which are holomorphic outside a certain set of points (markings) are studied. By an algebraic geometric degeneration process certain…

The subject of this paper is the problem of arrangement of a real nonsingular algebraic curve on a real non-singular algebraic surface. This paper contains new restrictions on this arrangement extending Rokhlin and Kharlamov-Gudkov-Krakhnov…

We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it…

We prove an analogue of E. Levi's Continuity Principle for meromorphic mappings with values in arbitrary compact complex manifolds in place of the Riemann sphere $\cc\pp^1$. The result is achieved by introducing a new extension method for…

We study continuity and regularity of convex extensions of functions from a compact set $C$ to its convex hull $K$. We show that if $C$ contains the relative boundary of $K$, and $f$ is a continuous convex function on $C$, then $f$ extends…

In this paper, we consider a non-degenerate CR manifold (M,H(M),J) with a given pseudo-Hermitian 1-form {\theta}, and endow the CR distribution H(M) with any Hermitian metric h instead of the Levi form L_{{\theta}}. This induces a natural…

We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on ${\Bbb C}^n\times{\Bbb C}^n$ with values in ${\Bbb R}^k$ is canonically isomorphic to the Lie algebra of infinitesimal holomorphic…

We consider a compact CR manifold with a transversal CR locally free circle action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szeg\H{o} kernel of the CR sections in the high tensor powers admits a…

We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic K\"ahler side in terms of the initial…

General expressions are given for the coefficients of Chern forms up to the 13th order in curvature in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for…

In this paper we prove, using a refinement of Terracini's Lemma, a sharp lower bound for the degree of (higher) secant varieties to a given projective variety, which extends the well known lower bound for the degree of a variety in terms of…

The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.

We consider a regular distribution $\mathcal{D}$ in a Riemannian manifold $(M,g)$. The Levi-Civita connection on $(M,g)$ together with the orthogonal projection allow to endow the space of sections of $\mathcal{D}$ with a natural covariant…

We study Segre varieties associated to Levi-flat subsets in complex manifolds and apply them to establish local and global results on the integration of tangent holomorphic foliations.