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E. A. Sevost'yanov

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

31 records · Page 2Linked to original sources
arXiv2018

On convergence of mappings in metric spaces with direct and inverse modulus conditions

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 mapping, whenever a function which corresponds to distortion of families of curves, is of finite mean oscillation at every point. Besides that, for one class of homeomorphisms of metric spaces, there are obtained theorems about equicontinuity of inverse mappings.

math.MG↗
arXiv2017

On Sokhotski--Casorati--Weierstrass theorem on metric spaces

In a neighborhood of isolated point of a domain of a metric space, a behavior of generalized quasiconformal mappings is studied. It is proved that, mappings mentioned above have continuous extension to the domain at some additional conditions. As consequence, an analog of Sokhotski--Weierstrass theorem is obtained.

math.CV↗
arXiv2017

On boundary behavior of mappings on Riemannian manifolds in terms of prime ends

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 classes mentioned above. In the terms mentioned above, there are obtained results about equicontinuity of these classes in the closure of the domain.

math.CV↗
arXiv2017

On equicontinuity of mappings in a case of variable domains

We study a local behavior of one class of mappings, which are defined in a domain of $n$-measured Euclidean space, in a case, when corresponding images of this domain are variable. Under some conditions on a function defining a behavior of mappings mentioned above, and some restrictions on mapped domains, the equicontinuity of the corresponding family of the mappings in the closure of the initial domain is proved.

math.CV↗
arXiv2016

On removability of isolated singularities of classes Orlicz - Sobolev

We study the local behavior of the closed-open discrete maps of Orlich--Sobolev classes in ${\Bbb R}^n,$ $n\geqslant 3.$ It was found that these mappings $f$ have continuous extension in isolated point $x_0$ in $D\setminus\{x_0 \},$ as soon as their dilatation of order $p\in (n-1, n] $ has the majorant of class $FMO$ at said point, and moreover, limits set of mapping $f$ at $x_0$ and $\partial D$ are disjoint.

math.CV↗
arXiv2016

On equicontinuity of inverse mappings in a closure of a domain

For some class of mappings satisfying upper modular estimates with respect to families of curves, a behavior of the corresponding inverse mappings is investigated. In the terms of prime ends, it is proved that, families of such homeomorphisms are equicontinuous (normal) in the closure of a given domain.

math.MG↗
arXiv2016

On equicontinuity of Sobolev classes in domains with locally connected boundary

A behavior of homeomorphisms of Orlicz classes in a closure of a domain is investigated. It is proved that above classes are equicontinuous in the closure of domains with some restrictions on it's boundaries provided that the corresponding inner dilatation of order $p$ has a majorant of finite mean oscillation at every point.

math.CV↗
arXiv2015

On absolute continuity for mappings, distorting moduli of cylinders

In the present paper, mappings satisfying one modular inequality with respect to cylinders in a space, are considered. Distorting of modulus is majorized by an integral which depends from some locally integrable function. The result on absolute continuity on lines of the functions mentioned above is proved

math.CV↗
arXiv2015

On boundary behavior of open discrete mappings on Riemannian manifolds

For some class of mappings, there are investigated problems connected with a possibility of continuous extension to a boundary on Riemannian manifolds. In particular, for so-called ring mappings, there is proved a result related to continuous extension to an isolated boundary point. Besides that, similar theorems hold for more general boundaries. As application of developed technique, there is proves a theorem about continuous extension of mapping of Orlicz--Sobolev class to an isolated singularity.

math.CV↗
arXiv2015

On local properties of one class of mappings on Riemannian manifolds

The present paper is devoted to questions located at the junction of the theory of space quasiconformal mappings and Riemannian surfaces. Theorems on local behavior of one class of open discrete mappings with unbounded characteristic of quasiconformality on arbitrary Riemannian manifolds are obtained

math.CV↗