Related papers: Extension of CR-functions on wedges

We show that every CR-automorphism of the closure of a Levi degenerate hyperquadric in the projective space extends to a holomorphic automorphism of the projective space.

Let M of real dimension 2n-1 be a compact, orientable, weakly pseudoconvex manifold of dimension at least five, embedded in C^N (n less than or equal to N), of codimension one or more in C^N, and endowed with the induced CR structure. We…

We explore connections between geometric properties of the Levi foliation of a Levi-flat hypersurface M and holomorphic convexity of compact sets in M, or bounded in part by M. Applications include extendability of Cauchy-Riemann functions,…

The behavior of the electromagnetic field near a common edge of a resistive half-plane and a perfectly conducting wedge is investigated. The possible appearance besides power terms also of logarithmic functions in the field expansions at…

The Torsion Anomalous Conjecture states that an irreducible variety $V$ embedded in a semi-abelian variety contains only finitely many maximal $V$-torsion anomalous varieties. In this paper we consider an irreducible variety embedded in a…

We study normal CR compact manifolds in dimension 3. For a choice of a CR Reeb vector field, we associate a Sasakian metric on them, and we classify those metrics. As a consequence, the underlying manifolds are topologically finite quotiens…

We introduce a new geometrical invariant of CR manifolds of hypersurface type, which we dub the "Levi core" of the manifold. When the manifold is the boundary of a smooth bounded pseudoconvex domain, we show how the Levi core is related to…

For a large class of convex domains in $\bf C^n$, it is shown that an $L^p$ function on the boundary is CR if there are holomorphic extensions on almost all slices of D by complex lines parallel to the coordinate axes. As an application, a…

Let $Gr$ be a component of the Grassmann manifold of a $C^*$-algebra, presented as the unitary orbit of a given orthogonal projection $Gr=Gr(P)$. There are several natural connections in this manifold, and we first show that they all agree…

We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c\`{a}dl\`{a}g functions endowed with the so-called weak M1…

Let M be a CR submanifold of maximal CR dimension of a complex space form M. The shape operator A of the distinguished vector field {\xi} is recurrent if there exists a 1-form v such that \nabla A = A \otimes v. We show that M is an…

For a real valued function defined on a compact set $K \subset \mathbb{R}^m$, the classical Whitney Extension Theorem from 1934 gives necessary and sufficient conditions for the existence of a $C^k$ extension to $\mathbb{R}^m$. In this…

Consider a compact Lie group $G$ and a closed Lie subgroup $H<G$. Let $\mathcal M$ be the set of $G$-invariant Riemannian metrics on the homogeneous space $M=G/H$. By studying variational properties of the scalar curvature functional on…

In this paper we extend Witten-Helffer-Sj\"ostrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we…

We prove some Liouville-type theorems for positive harmonic functions on compact Riemannian manifolds with nonnegative Ricci curvature and strictly convex boundary, thereby confirming some cases of Wang's conjecture (J. Geom. Anal. 31,…

We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by…

In this paper, we propose a generalization of the Riemann curvature tensor on manifolds (of dimension two or higher) endowed with a Regge metric. Specifically, while all components of the metric tensor are assumed to be smooth within…

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,…

Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient…

We construct knot invariants on the basis of ascribing Euclidean geometric values to a triangulation of sphere S^3 where the knot lies. The main new feature of this construction compared to the author's earlier papers on manifold invariants…