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On lower distance estimates of mappings in metric spaces
Evgeny Sevost'yanov, Denys Romash, Nataliya Ilkevych
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applicati…
On the prime ends extension of unclosed inverse mappings
Evgeny Sevost'yanov, Victoria Desyatka Zarina Kovba
We consider mappings that distort the modulus of families of paths in the opposite direction in the manner of Poletsky's inequality. Here we study the case when the mappings are no…
On the lower bounds of -modulus of families of paths and a finite connectedness
Evgeny Sevost'yanov, Zarina Kovba, Heorhii Nosal +1
We study the problem of the lower bounds of the modulus of families of paths of order and their connection with the geometry of domains containing the specified famil…
On convergence of homeomorphisms with inverse modulus inequality
Evgeny Sevost'yanov, Valery Targonskii
We have studied homeomorphisms that satisfy the Poletsky-type inverse inequality in the domain of the Euclidean space. It is proved that the uniform limit of the family of such hom…
An analogue of Koebe's theorem and the openness of a limit map in one class
Evgeny Sevost'yanov, Valery Targonskii
We study mappings that satisfy the inverse modulus inequality of Poletsky type in a fixed domain. It is shown that, under some additional restrictions, the image of a ball under su…
On convergence of a sequence of mappings with inverse modulus inequality to a discrete mapping
E. O. Sevost'yanov, V. A. Targonskii
We have studied the mappings that satisfy the Poletsky-type inverse inequality in the domain of the Euclidean space. It is proved that the uniform boundary of the family of such ma…
On quasilinear Beltrami equations with restrictions on tangential dilatation
E. O. Sevost'yanov, V. A. Targonskii, N. S. Ilkevych
We study quasilinear Beltrami equations, the complex coefficients of which depend on the unknown function. In terms of the so-called tangential dilatation, we have found conditions…