相关论文: Prime ends for domains in metric spaces
By using the inner diameter distance condition we define and investigate new, in such a generality, class $\mathcal{F}$ of homeomorphisms between domains in metric spaces and show that, under additional assumptions on domains, $\mathcal{F}$…
We study mappings defined in the domain of a metric space that distort the modulus of families of paths by the type of the inverse Poletskii inequality. Under certain conditions, it is proved that such mappings have a continuous extension…
In this note we study the Dirichlet problem associated with a version of prime end boundary of a bounded domain in a complete metric measure space equipped with a doubling measure supporting a Poincare inequality. We show the resolutivity…
We investigate prime ends in the Heisenberg group $\mathbb{H}_{1}$ extending N\"akki's construction for collared domains in Euclidean spaces. The corresponding class of domains is defined via uniform domains and the Loewner property. Using…
It is given a canonical representation of prime ends in regular spatial domains and, on this basis, it is studied the boundary behavior of the so-called lower Q-homeomorphisms that are the natural generalization of the quasiconformal…
We study mappings that satisfy the inverse Poletsky inequality in a domain of the Euclidean space. Under certain conditions on the definition and mapped domains, it is established that they have a continuous extension to the boundary in…
We prove a Carath\'eodory-type extension of BQS homeomorphisms between two domains in proper, locally path-connected metric spaces as homeomorphisms between their prime end closures. We also give a Carath\'eodory-type extension of geometric…
We study local connectedness, local accessibility and finite connectedness at the boundary, in relation to the compactness of the Mazurkiewicz completion of a bounded domain in a metric space. For countably connected planar domains we…
The paper is devoted to the study of the boundary behavior of mappings. We consider mappings that satisfy inverse moduli inequalities of Poletskii type, under which the images of the domain under the mappings may change. It is proved that a…
Prime end boundaries $\partial_P\Omega$ of domains $\Omega$ are studied in the setting of complete doubling metric measure spaces supporting a $p$-Poincar\'e inequality. Notions of rectifiably (in)accessible- and (in)finitely far away prime…
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…
The paper is devoted to the study of mappings with finite distortion, actively studied recently. For mappings whose inverse satisfy the Poletsky inequality, the results on boundary behavior in terms of prime ends are obtained. In…
We study the boundary behavior of the so-called ring $Q$-mappings obtained as a natural generalization of mappings with bounded distortion. We establish a series of conditions imposed on a function $Q(x)$ for the continuous extension of…
We study problems related to continuous boundary extension of mappings of Orlicz-Sobolev classes in terms of prime ends. The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the…
The article is devoted to the study of mappings that distort the modulus of families of paths by the Poletsky inequality type. At boundary points of a domain, we have obtained the H\"{o}lder inequality for such mappings, provided that their…
We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.
For mapping with branching points that satisfy the inverse inequality of Poletsky, we obtained the results of their continuous boundary extension in terms of prime ends. Under certain conditions, the specified classes od mappings are also…
In this paper we introduce a new class of domains in complex Euclidean space, called Goldilocks domains, and study their complex geometry. These domains are defined in terms of a lower bound on how fast the Kobayashi metric grows and an…
We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification is given in terms of rationality of Carath\'eordory's prime…
We consider mappings that distort the modulus of families of paths in the opposite direction in the manner of Poletsky's inequality. Here we study the case when the mappings are not closed, in particular, they do not preserve the boundary…