Related papers: On ring homeomorphisms with inverse modulus condit…
In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems…
First of all, we prove that open mappings in Orlicz-Sobolev classes $W^{1,\phi}_{\rm loc}$ under the Calderon type condition on $\phi$ have the total differential a.e. that is a generalization of the well-known theorems of…
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 show how a parameterized family of maps of the spine of a manifold can be used to construct a family of homeomorphisms of the ambient manifold which have the inverse limits of the spine maps as global attractors. We describe applications…
We show that homeomorphisms $f$ in ${\Bbb R}^n$, $n\geqslant3$, of finite distortion in the Orlicz--Sobolev classes $W^{1,\varphi}_{\rm loc}$ with a condition on $\varphi$ of the Calderon type and, in particular, in the Sobolev classes…
Inverse semigroups are a class of semigroups whose structure induces a compatible partial order. This partial order is examined so as to establish mirror properties between an inverse semigroup and the semilattice of its idempotent…
We study the quasi-endomorphism ring of infinitely definable subgroups in separably closed fields. Based on the results we obtain, we are able to prove a Mordell-Lang theorem for Drinfeld modules of finite characteristic. Using…
We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of…
We construct a cycle class map from the higher Chow groups of 0-cycles to the relative $K$-theory of a modulus pair. We show that this induces a pro-isomorphism between the additive higher Chow groups of relative 0-cycles and relative…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
We study the so--called ring $(p,Q)$--mappings which are the natural generalization of quasiregular and quasi isometric mappings. It is proved that open discrete ring $(p,Q)$--mappings are differentiable a.e. and belong to the class $ACL$…
It is founded the sufficient condition of Holder continuity of the ring $Q$-homeomorphisms in $\mathbb{R}^n, n\geq 2$ with respect to $p$-modulus at $n-1<p<n$.
It is known that automorphisms of quasi-circular domains fixing the origin are polynomial mappings. By introducing the so-called resonance order and quasi-resonance order, we provide a uniform upper bound for the degree of such polynomial…
We show that a generic quasiperiodically forced circle homeomorphism is mode-locked: the rotation number in the fibres is rationally related to the rotation number in the base and it is stable under small perturbations of the system. As a…
We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasi-homomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping…
We show that every homeomorphic $W^{1,1}_{\rm loc}$ solution $f$ of a Beltrami equation $\overline{\partial}f=\mu\,\partial f$ in a domain $D\subseteq\Bbb C$ is the so--called ring $Q-$homeomorphism with $Q(z)=K^T_{\mu}(z, z_0)$ where…
For mappings in metric spaces satisfying one inequality with respect to modulus of families of curves, there is proved a lightness of the uniform limit of these mappings. It is proved that, the uniform limit of these mappings is light…
Beardon and Minda gave a characterization of normal families of holomorphic and meromorphic functions in terms of a locally uniform Lipschitz condition. Here, we generalize this viewpoint to families of mappings in higher dimensions that…
The global homeomorphism theorem for quasiconformal maps describes the following specifically higher-dimensional phenomenon: {\em Locally invertible quasiconformal mapping $f: {\R}^{n} \to {\R}^{n}$ is globally invertible provided $n > 2$.}…
We study branching mappings that satisfy some condition of distortion of the modulus of families of paths. In a situation where the definition domain of mappings is locally connected on its boundary, the mapped domain is regular, and the…