Related papers: A general version of the Hartogs extension theorem…

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…

Let F_*(X, Y) be the space of base-point-preserving maps from a connected finite CW complex X to a connected space Y. Consider a CW complex of the form X cup_{alpha}e^{k+1} and a space Y whose connectivity exceeds the dimension of the…

We show that for every connected analytic subvariety $V$ there is a pseudoconvex set $\Omega$ such that every bounded matrix-valued holomorphic function on $V$ extends isometrically to $\Omega$. We prove that if $V$ is two analytic disks…

Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of…

We introduce the class of compactly H\"older mappings between metric spaces and determine the extent to which they distort the Minkowski dimension of a given set. These mappings are defined purely with metric notions and can be seen as a…

If $A$ is an algebra with finite right global dimension, then for any automorphism $\alpha$ and $\alpha$-derivation $\delta$ the right global dimension of $A[t; \alpha, \delta]$ satisfies \[ \text{rgld} \, A \le \text{rgld} \, A[t; \alpha,…

Let $X, Y$ be two complex manifolds of dimension 1 which are countable at infinity, let $D\subset X,$ $ G\subset Y$ be two open sets, let $A$ (resp. $B$) be a subset of $\partial D$ (resp. $\partial G$), and let $W$ be the 2-fold cross…

We give direct proofs and constructions of the trace and extension theorems for Sobolev mappings in $W^{1, 1} (M, N)$, where $M$ is Riemannian manifold with compact boundary $\partial M$ and $N$ is a complete Riemannian manifold. The…

We study the analytic continuation problem for a germ of a biholomorphic mapping from a non-minimal real hypersurface $M\subset\CC{n}$ into a real hyperquadric $\mathcal Q\subset\CP{n}$ and prove that under certain non-degeneracy conditions…

This paper generalises the result of Jean-Pierre Demailly on his Ohsawa--Takegoshi-type $L^2$ extension theorem, which guarantees holomorphic extensions for some sections $f$ on analytic subspaces $Y$ defined by multiplier ideal sheaves of…

In a neighborhood of isolated point of a domain of a metric space, a behavior of generalized quasiconformal mappings is studied. It is proved that, mappings mentioned above have continuous extension to the domain at some additional…

We develop a theory of $\times$-homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that $\times$-homotopies from finite graphs can be decomposed…

This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the…

We derive a quasiconformal extension to 3-space of the Weierstrass-Enneper lifts of a class of harmonic mappings defined in the unit disk. The extension is based on fibrations of space by circles in domain and image that correspond to each…

Let $(V,\omega)$ be a compact K\"ahler manifold such that $V$ admits a cover by Zariski-open Stein sets with the property that $\omega$ has a strictly plurisubharmonic exhaustive potential on each element of the cover. If $X\subset V$ is an…

A direct application of Zorn's Lemma gives that every Lipschitz map $f:X\subset \mathbb{Q}_p^n\to \mathbb{Q}_p^\ell$ has an extension to a Lipschitz map $\widetilde f: \mathbb{Q}_p^n\to \mathbb{Q}_p^\ell$. This is analogous, but more easy,…

Given a Moebius homeomorphism $f : \partial X \to \partial Y$ between boundaries of proper, geodesically complete CAT(-1) spaces $X,Y$, we describe an extension $\hat{f} : X \to Y$ of $f$, called the circumcenter map of $f$, which is…

We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…

We consider a compact $C^\omega$ manifold $X$ and finitely many regular $C^\omega$ submanifolds $Y_1, \dots, Y_q$ of $X$, which are closed subsets in $X$, such that the union of $Y_j$'s has only normal crossings. We show that every…

We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains $C$, with non-smooth boundary, in possibly non-compact manifolds. Assuming $C$ is a submanifold with corners, or…