Related papers: Mappings with the inverse Poletsky inequality are …
Under a plausible geometric hypothesis, we show that a biholomorphic mapping of smoothly bounded, pseudoconvex domains extends to a diffeomorphism of the closures.
For mappings in metric spaces satisfying one inequality with respect to modulus of families of curves, there is proved a lightness of preimage under the mapping. It is proved that, the mappings, satisfying estimate mentioned above, are…
We study the topological invariant $\phi$ of Kwieci\'nski and Tworzewski, particularly beyond the case of mappings with smooth targets. We derive a lower bound for $\phi$ of a general mapping, which is similarly effective as the upper bound…
In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary and moreover these extensions are…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We announce…
In this paper, we consider boundary extensions of two classes of mappings between metric measure spaces. These two mapping classes extend in particular the well-studied geometric mappings such as quasiregular mappings with integrable…
We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities,…
We consider various metric and analytic notions of finiteness on translation surfaces. The Veech group of a surface is discrete if the surface has finite area or is totally bounded.
We establish the existence and uniqueness of limits at infinity along infinite curves outside a zero modulus family for functions in a homogeneous Sobolev space under the assumption that the underlying space is equipped with a doubling…
We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.
The paper is devoted to the study of mappings satisfying the inverse Poletsky inequality. We study the local behavior of these mappings, moreover, we are most interested in the case when the corresponding majorant is integrable on some set…
We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian…
In this article, we investigate the relationship between the shadowing property of set-valued maps and their associated inverse limit systems. We show that if a set-valued map is expansive and open in the context of set-valued dynamics,…
This article is devoted to the study of mappings with branch points whose characteristics satisfy integral-type constraints. We have proved theorems concerning their local and global behavior. In particular, we established the…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for zero-dimensional spaces in terms of regular extension operators having compact…
The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity properties of the original, has proven crucial in our…
We show that the typical nonexpansive mapping on a small enough subset of a CAT($\kappa$)-space is a contraction in the sense of Rakotch. By typical we mean that the set of nonexpansive mapppings without this property is a $\sigma$-porous…
This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces,…
A boundary behavior of ring mappings on Riemannian manifolds, which are generalization of quasiconformal mappings by Gehring, is investigated. In terms of prime ends, there are obtained theorems about continuous extension to a boundary of…