Equicontinuity by the prime ends of mappings with the normalization condition

关于通过可变域的素端的映射等度连续性的研究

On equicontinuity of mappings with inverse moduli inequalities by prime ends of variable domains

本文研究了满足Poletskii型逆模不等式的映射的边界行为，证明了在模不等式中的主量可积时，某些类别的此类映射相对于某些域的素端是等度连续的。

On equicontinuity of Orlicz--Sobolev class in s closure of a domain

A behavior of homeomorphisms of Orlicz--Sobolev classes in a closure of a domain is investigated. There are obtained theorems about equicontinuity of classes mentioned above in terms of prime ends of regular domains. In particular, it is proved that above classes are equicontinuous in 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.

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.

On equicontinuity of families of mappings with a fixed point of a domain

The behavior of a class of mappings of a domain of Euclidean space is studied. It is established that the indicated class is equicontinuous both at the inner and at the boundary points of the domain if the mappings contained in it satisfy the general normalization condition, and the corresponding characteristic of quasiconformality has a weak growth.

关于非闭逆映射的素端延拓

On the prime ends extension of unclosed inverse mappings

本文研究满足Poletsky不等式逆形式的非闭映射，在特定条件下证明了其在素端意义下的连续边界延拓及映射族的等度连续性。

关于开离散非闭映射的卡拉泰波利定理

On Caratheodory theorem for open discrete unclosed mappings

研究满足逆波雷斯基不等式的映射，探讨其在非局部连通边界下的等连续性及Orlicz-Sobolev类对应性质。