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E. Sevost'yanov

Publications and source records attributed to E. Sevost'yanov.

10 recordsLinked to original sources
arXiv2026

On the global behavior of mappings and the correspondence of boundaries

We consider families of mappings with moduli inequalities, having different definition domains. Under some additional assumptions we have proved that such families are uniformly equicontinuous. We have considered four main cases: when mappings are homeomorphisms and corresponding domains have simple geometry; when similar mappings have branch points; when domains with complex geometry are considered, but mappings still are homeomorphisms; and when similar mappings have branch points. Sequences of domains are generally assumed to converge to a kernel, and the characteristics of the mappings must satisfy certain conditions on their growth. In some of the four cases mentioned above, we also described properties of the limit mapping. We also obtained the correspondence of the boundary points of the kernel to the boundary points, and the inner points to the inner points.

math.CV↗
arXiv2026

On uniformly lightness of one class of mappings and Koebe-Bloch theorem

We consider mappings satisfying a certain estimate of the distortion of the modulus of families of paths, similar to the geometric definition of quasiconformal mappings. Under appropriate restrictions, we show that the class of such mappings is uniformly light, i.e., the chordal diameter of the image of continua whose diameter is bounded below is also bounded below uniformly over the class. Under some even greater restrictions, we establish some more explicit estimates of the distortion of the diameters of these continua.

math.CV↗
arXiv2021

On compact classes of solutions of Dirichlet problem in simply connected domains

The article is devoted to questions concerning the problems of compactness of solutions of the Dirichlet problem for the Beltrami equation in some simply connected domain. In terms of prime ends, we have proved results of a detailed form for the case when the maximal dilations of these solutions satisfy certain integral constraints. In addition, in this article we have proved theorems on the local and global behavior of plane and spatial mappings with direct and inverse modulus conditions.

math.CV↗
arXiv2020

Logarithmic Holder continuous mappings and Beltrami equation

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 of spheres of positive linear measure. The most important result is a logarithmic Hölder continuity of such mappings at inner points. As a corollary, we obtained the existence of a continuous $ACL$-solution of the Beltrami equation, which is logarithmic Hölder continuous.

math.CV↗
arXiv2019

On Poletsky type inequality for mappings of Riemannian surfaces

In this paper, we obtain upper estimates for the distortion of the modulus of families of paths under mappings of the Sobolev class, whose dilatation is locally integrable. As a consequence, theorems on the local and boundary behavior of the indicated mappings are obtained.

math.CV↗
arXiv2019

On Hölder continuity of mappings in domains and on boundaries

We study mappings with branching of a domain of Euclidean space. The Hölder and Lipschitz continuity are established for one class of spatial mappings whose characteristic satisfies the Dini type condition in a given domain. In addition, we found conditions on the complex coefficient of the degenerate Beltrami equations in the unit disk under which generalized homeomorphic solutions of this equation are Hölder continuous at the points of the boundary.

math.CV↗
arXiv2017

On boundary extension of mappings in metric spaces in terms of prime ends

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 given mappings with respect to prime ends in domains with regular boundaries in metric spaces.

math.CV↗
arXiv2010

On equicontinuity of homeomorphisms with finite distortion in the plane

It is stated equicontinuity and normality of families $\frak{F}^Φ$ of the so--called homeomorphisms with finite distortion on conditions that $K_{f}(z)$ has finite mean oscillation, singularities of logarithmic type or integral constraints of the type $\intΦ\left(K_{f}(z)\right)dx\,dy<\infty$ in a domain $D\subset{\C}.$ It is shown that the found conditions on the function $Φ$ are not only sufficient but also necessary for equicontinuity and normality of such families of mappings.

math.CV↗
arXiv2010

Equicontinuity of mappings quasiconformal in the mean

It is stated a series of criteria of equicontinuity and normality for classes of space mappings with integral restrictions. It is shown that the found conditions are not only sufficient but also necessary. It is given applications to Sobolev's classes.

math.CV↗