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Article
On the Existence of Solutions of Quasilinear Beltrami Equations with Two Characteristics
We study Beltrami-type equations with two given complex characteristics. Under certain conditions imposed on the complex coefficients, we prove theorems on the existence of homeomorphic ACL-solutions of this equa...
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Article
On Equicontinuity of the Families of Map**s with One Normalization Condition in Terms of Prime Ends
We study map**s with branching satisfying certain conditions of distortion for the modulus of families of paths. Under the conditions that the domain of definition of map**s has a weakly flat boundary, the...
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Article
Boundary Extensions of Map**s Satisfying the Poletsky Inverse Inequality in Terms of Prime Ends
For map**s with branching points satisfying the Poletsky inverse inequality, we obtain some results on their continuous boundary extensions in terms of prime ends. Under certain restriction, the indicated cl...
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Article
On Orlicz–Sobolev Classes on Quotient Spaces
We study the quotient spaces of the unit ball by some group of Möbius transformations. For map**s of such spaces, we obtain a bound for the distortion of a modulus of a family of spheres. As an application,...
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Article
On Equicontinuous Families of Map**s of Metric Spaces
We obtain analogs of the results on equicontinuity of families of quasiregular map**s that take no values from a fixed continuum. We prove that these families are equicontinuous whenever the quasiconformalit...
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Article
Equicontinuity of Families of Map**s with One Normalization Condition
We study the behavior of a certain class of map**s of a domain in Euclidean space. We prove that this class is equicontinuous both at the interior and boundary points, of the domain provided that it consi...
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Article
On a Poletskii-Type Inequality for Map**s of the Riemannian Surfaces
We establish upper estimates for the distortion of the modulus of families of curves under map**s from the Sobolev class whose dilatation is locally integrable. As a consequence, we prove theorems on the loc...
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Article
On the Equicontinuity of Families of Map**s in the Case of Variable Domains
We study the problem of local behavior of maps in the closure of a domain in the Euclidean space. The equicontinuity of families of these map**s is established in the case where the mapped domain is not fixe...
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Article
On the Local Behavior of Sobolev Classes on Two-Dimensional Riemannian Manifolds
We study open discrete maps of two-dimensional Riemannian manifolds from the Sobolev class. For these map**s, we establish the lower estimates of distortions of the moduli of families of the curves. As a con...
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Article
On the Lower Estimate of the Distortion of Distance for One Class of Map**s
We study the behavior of one class of map**s with finite distortion in the vicinity of the origin. Under certain conditions imposed on the characteristic of quasiconformality, we establish a lower estimate f...
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Article
On the Equicontinuity of One Family of Inverse Map**s in Terms of Prime Ends
For a class of map**s satisfying upper modular estimates with respect to the families of curves, we study the local behavior of the corresponding inverse map**s. In terms of prime ends, we prove that the f...
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Article
On the Convergence of Map**s in Metric Spaces with Direct and Inverse Modulus Conditions
For map**s in metric spaces satisfying one inequality for the modulus of families of curves, we establish the property of lightness of the limit map**. It is shown that the uniform limit of these map**s ...
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Article
On the Equicontinuity of Homeomorphisms of Orlicz and Orlicz–Sobolev Classes in the Closure of a Domain
We study the behavior of homeomorphisms of Orlicz–Sobolev classes in the closure of a domain. The theorems on equicontinuity of the indicated classes are obtained in terms of the prime ends of regular domains....
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Article
On the Absolute Continuity of Map**s Distorting the Moduli of Cylinders
We consider map**s satisfying one modular inequality with respect to cylinders in the space. The distortion of the modulus is majorized by an integral depending on a certain locally integrable function. We a...
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Article
On the zero-dimensionality of the limit of the sequence of generalized quasiconformal map**s
The paper is devoted to the study of the properties of a class of space map**s that is more general than that of bounded distortion map**s (aka quasiregular map**s). It is shown that the locally uniform ...
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Article
On the Equicontinuity of Map**s with Branching in the Closure of the Domain
We study the problem of local behavior of map**s f : D → ...
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Article
On local properties of spatial generalized quasi-isometries
An upper bound for the measure of the image of a ball under map**s of a certain class generalizing the class of branched spatial quasi-isometries is determined. As a corollary, an analog of Schwarz’ classica...
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Article
On the Local Behavior of Open Discrete Map**s from the Orlicz–Sobolev Classes
The paper is devoted to the study of map**s with unbounded characteristic of quasiconformality and, in particular, of map**s with finite distortion, which are now extensively studied. We establish theorems...
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Article
On the Removability of Isolated Singularities of Orlicz–Sobolev Classes with Branching
We study the local behavior of closed-open discrete map**s of the Orlicz–Sobolev classes in ...
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Article
Normality of the Orlicz–Sobolev Classes
We establish a series of new criteria of equicontinuity and, hence, normality of the map**s of Orlicz–Sobolev classes in terms of inner dilatations.
