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S. A. Skvortsov

Publications and source records attributed to S. A. Skvortsov.

5 recordsLinked to original sources
arXiv2018

On behavior of a class of mappings in terms of prime ends

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 particular, it was proved that the families of the indicated mappings are equicontinuous at the points of the boundary if a certain function determining the distortion of the module under the mappings is integrable in a given domain.

math.CV↗
arXiv2017

On behavior of homeomorphisms with inverse modulus conditions

We consider some class of homeomorphisms of domains of Euclidean space, which are more general than quasiconformal mappings. For these homeomorphisms, we have obtained theorems on local behavior of it's inverse mappings in a given domain. Under some additional conditions, we proved results about behavior of mappings mentioned above in the closure of the domain.

math.MG↗
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↗
arXiv2015

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↗