Related papers: A note on CR mappings of positive codimension

Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie…

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…

Let $q$ be a positve integer, and $G$ be a $q$-partite simple graph on $qn$ vertices, with $n$ vertices in each vertex class. Let $\delta={k_q \over k_q+1}$, where $k_q=q+O(\log{q})$. If each vertex of $G$ is adjacent to at least $\delta n$…

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group $A(\Gamma)$ fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups $\text{Mod}(S)$. In…

We construct examples of $C^\infty$ smooth submanifolds in ${\Bbb C}^n$ and ${\Bbb R}^n$ of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact…

We call a subset $K$ of $\mathbb C$ \emph{biholomorphically homogeneous} if for any two points $p,q\in K$ there exists a neighborhood $U$ of $p$ and a biholomorphism $\psi:U\to \psi(U)\subset \mathbb C$ such that $\psi(p)=q$ and $\psi(K\cap…

For positive integers $k < n$ such that $k$ divides $n$, let $(n)^k_{\hom}$ be the set of homogeneous $k$-partitions of $\{1, \dots, n\}$, that is, the set of partitions of $\{1, \dots, n\}$ into $k$ classes of the same cardinality. In the…

We prove an analogue of the L\"uck Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin groups and Bestvina--Brady groups. Specifically, we prove that…

It is proved that the germ of a holomorphic map from a real analytic hypersurface M in C^n into a strictly pseudoconvex compact real algebraic hypersurface M' in C^N, 1 < n < N extends holomorphically along any path on M.

Let f : (M,p)\to (M',p') be a formal (holomorphic) nondegenerate map, i.e. with formal holomorphic Jacobian J_f not identically vanishing, between two germs of real analytic generic submanifolds in \C^n, p'=f(p). Assuming the target…

Let $X$ be a CR manifold with transversal, proper CR $G$-action. We show that $X/G$ is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold…

Let $M\subset \mathbb{C}^{n+1}$ ($n\geq 2$) be a real analytic submanifold defined by an equation of the form: $w=|z|^2+O(|z|^3)$, where we use $(z,w)\in \mathbb{C}^{n}\times \mathbb{C}$ for the coordinates of $\mathbb{C}^{n+1}$. We first…

We show that every formal embedding sending a real-analytic strongly pseudoconvex hypersurface in $M\subset \C^N$ into another such hypersurface in $M'\subset \C^{N+1}$ is convergent. More generally, if $M$ and $M'$ are merely…

We construct quasi-isometric embeddings from right-angled Artin groups into the outer automorphism group of a free group. These homomorphisms are in analogy with those constructed in \cite{CLM}, where the target group is the mapping class…

In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led…

Let $Y\subset{\mathbb R}^n$ be a triangulable set and let $r$ be either a positive integer or $r=\infty$. We say that $Y$ is a $\mathscr{C}^r$-approximation target space, or a $\mathscr{C}^r\text{-}\mathtt{ats}$ for short, if it has the…

Let X, Y be nonsingular real algebraic sets. A map fi:X-->Y is said to be k-regulous, where k is a nonnegative integer, if it is of class C^k and the restriction of fi to some Zariski open dense subset of X is a regular map. Assuming that Y…

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.…

The first part of this article is devoted to the study families of totally real intersecting $n$-submanifolds of $(\Bbb C^n,0)$. We give some conditions which allow to straighten holomorphically the family. If this is not possible to do it…

Let R be an excellent local ring, m its maximal ideal and I an ideal. Then there exists a positive integer c such that for all integers n, the integral closure of (I + m^n) is contained in m^(n/c) + the integral closure of I. In the proof,…