Related papers: Prime ends in metric spaces and boundary extension…
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…
In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carath\'eodory and N\"akki. Modulus ends and prime ends, defined by means of the…
It is proved criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between domains on the Riemann surfaces by prime ends of Caratheodory.
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 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…
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…
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 non-homeomorphic mappings of Riemannian surfaces of Sobolev class. We have obtained some estimates of distortion of moduli of families of curves. We have proved that, under some conditions, these mappings have a continuous…
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 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 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…
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…
It is established a series of criteria for continuous and homeomorphic extension to the boundary of the so-called lower $Q$-homeomorphisms $f$ between domains in $\overline{\Rn}=\Rn\cup\{\infty\}$, $n\geqslant2$, under integral constraints…
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…
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 provide several new examples in dynamics on the $2$-sphere, with the emphasis on better understanding the induced boundary dynamics of invariant domains in parametrized families. First, motivated by a topological version of the…
In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions…
A boundary behavior of mappings, which are closely related with Sobolev and Orlicz--Sobolev classes in the plane and in the space, is investigated. There are obtained theorems on boundary behavior of classes mentioned above.
We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…