Related papers: CR functions at CR singularities: approximation, e…
We introduce a notion of locally approximable continuous CR functions on locally closed subsets of reduced complex spaces, generalizing both holomorphic functions and CR functions on CR submanifolds. Under additional assumptions of…
Cartan's uniqueness theorem does not hold in general for CR mappings, but it does hold under certain conditions guaranteeing extendibility of CR functions to a fixed neighborhood. These conditions can be defined naturally for a wide class…
Real-analytic CR functions on real-analytic CR singular submanifolds are not in general restrictions of holomorphic functions, unlike in the CR nonsingular case. We give a simple condition that completely characterizes those quadric CR…
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…
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 establish the holomorphic wedge extendability of CR functions, defined on an everywhere locally minimal generic submanifold M of C^n and having singularities contained in a submanifold N of codimension 1, 2 or 3, assuming some…
We define a class of generic CR submanifolds of $C^n$ of real codimension $d$, with $d$ in $1, ..., n-1$, called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the…
In this paper, a generalization of the "sector property" theorem first pioneered by Baouendi, Rothschild and Treves is given. The main contribution consists in showing that if a submanifold of $\C^n$ with higher codimension is locally…
We characterize rotund, uniformly rotund, locally uniformly rotund and compactly locally uniformly rotund spaces in terms of sets of (almost) farthest points from the unit sphere using the generalized diameter. For this we introduce few…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the…
We study properties of functions with bounded variation in Carnot-Ca\-ra\-th\'eo\-do\-ry spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of…
We endeavour a systematic approach for the removal of singularities for CR functions on an arbitrary embeddable CR manifold.
In this paper we characterize sums of CR functions from competing CR structures in two scenarios. In one scenario the structures are conjugate and we are adding to the theory of pluriharmonic boundary values. In the second scenario the…
We give a constructive description of H{\"o}lder-like classes of functions on chord-arc curves in $\mathbb{R}^3$ in terms of a rate of approximation by harmonic functions in shrinking neighborhoods of those curve.
Motivated by the Shilov boundaries of bounded symmetric domains we consider arbitrary CR-quadrics in a complex linear space (of finite dimension) that have a certain symmetry property. For these the non-affine local CR-automorphisms have a…
We say that a CR singular submanifold $M$ has a removable CR singularity if the CR structure at the CR points of $M$ extends through the singularity as an abstract CR structure on $M$. We study such real-analytic submanifolds, in which case…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
A general class of singular real hypersurfaces, called subanalytic, is defined. For a subanalytic hypersurface M in C^n, Cauchy-Riemann (or simply CR) functions on M are defined, and certain properties of CR functions discussed. In…
We give a constructive description of H\"older-like classes of functions on a chord-arc curve in $\mathbb{R}^3$ by means of a rate of approximation by function harmonic is shrinking neibourhoods of those curve