arXiv subjects
Publications and source records attributed to Bogdan Klishchuk.
We consider the class of ring $Q$-homeomorphisms with respect to $p$-modulus in $\mathbb{R}^{n}$ with $p > n$, and obtain lower bounds for limsups of the distance distortions under such mappings. These estimates can be treated as Hölder's continuity of the inverses near the origin. The sharpness is illustrated by example
We study the behavior at infinity of ring $Q$-homeomorphisms with respect to $p$-modulus for $p>n$.
There were obtained some properties of weakly m-convex sets. Various kinds of the problem of shadow were investigated. There was obtained the lower estimation for the number of balls that are necessary to create a shadow at the point of the sphere in three-dimensional Euclidean space
In this article we consider Q-homeomorphisms with respect to the p-modulus on the complex plane with p>2. It is obtained a lower area estimate for image of discs under such mappings. We solved the extremal problem about minimization of the area functional of images of discs.
This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a coacute angle condition" or "a strict coacute angle condition". There also were obtained similar results for restrictions of multivalued mappings satisfying some metric limitations.