E. Sevost'yanov
In this paper, we obtain upper estimates for the distortion of the modulus of families of paths under mappings of the Sobolev class, whose dilatation is locally integrable. As a consequence, theorems on the local and boundary behavior of the indicated mappings are obtained.
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We study some problems related to the boundary behavior of maps of domains of Riemannian surfaces. In particular, for mappings satisfying the inverse Poletsky type modulus inequality, we establish the possibility of their continuous extension to the boundary in terms of prime ends. We also study the local behavior of such mappings at boundary points.
For mapping with branching points that satisfy the inverse inequality of Poletsky, we obtained the results of their continuous boundary extension in terms of prime ends. Under certain conditions, the specified classes od mappings are also equicontinuous in the closure of a given domain.
It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of the definition domain. Under some stronger conditions, we also have proved that it is open and discrete there.
On unclosed mappings with Poletsky inequality
本文研究满足加权 Poletsky 不等式的有限畸变映射，证明在边界有限连通且控制函数满足积分发散或有限平均振荡条件时，映射可连续延拓到边界。
This article is devoted to the study of mappings defined in the region on the plane. Under certain conditions, the upper estimate of the distortion of the modulus of families of paths is obtained. Similarly, the upper estimate of the modulus of the families of paths in the pre-image under the mapping is also obtained.
The article is devoted to establishing the distortion of the modulus of families of paths in wide classes of mappings that admit branch points. In particular, for mappings that are differentiable almost everywhere and have $N$- and $N^{\,- 1}$-Luzin properties and are absolutely continuous on almost all paths, we obtained the inverse Poletsky inequality with the so-called cotangent dilatation. We have proved that, for inverse mappings, this dilatation coincides with the so-called tangential dilatation of the corresponding inverse mapping. In addition, we have proved that cotangent dilatation i…
On distortion estimates of mappings with the Poletsky condition in domains with Poincare inequality
本文研究了满足 Poletsky 不等式条件的映射在边界点处的距离偏差估计，前提是像区域满足 Ahlfors 正则性和 Poincare 不等式，并探讨了同胚、分支映射及不同边界类型的定义域。
On boundary Hölder continuity of mappings with the Poletsky condition
本文研究了满足 Poletsky 不等式扭曲路径族模数的映射，在特征具有有限积分平均的条件下，证明了其在同胚与分支映射、良好边界与素端边界情形下的边界 Hölder 连续性。
We study mappings satisfying the so-called inverse Poletsky inequality. Under integrability of the corresponding majorant, it is proved that these mappings are logarithmic Hölder continuous in the neighborhood of the boundary points. In particular, the indicated properties hold for homeomorphisms whose inverse satisfy the weighted Poletsky inequality.
On the theory of generalized quasiconformal mappings
本文在逆 Poletsky 不等式框架下研究广义拟共形映射，分析其局部与边界行为，并证明该映射类具有对数 Hölder 连续性。
We study mappings that satisfy the inverse Poletsky inequality in a domain of the Euclidean space. Under certain conditions on the definition and mapped domains, it is established that they have a continuous extension to the boundary in terms of prime ends if the majorant involved in the Poletsky inequality is integrable over spheres. Under some additional conditions, the extension mentioned above is discrete.
On convergence of homeomorphisms with inverse modulus inequality
本文研究欧氏空间中满足Poletsky型逆不等式的同胚映射族，证明了其均匀极限只能是同胚映射或扩展空间中的常数。
We study mappings differentiable almost everywhere, possessing the $N$-Luzin property, the $ N^{\,-1}$-property on the spheres with respect to the $(n-1)$-dimensional Hausdorff measure and such that the image of the set where its Jacobian equals to zero has a zero Lebesgue measure. It is proved that such mappings satisfy the lower bound for the Poletsky-type distortion in their domain of definition.
On convergence of a sequence of mappings with inverse modulus inequality to a discrete mapping
研究 Euclid 空间中满足 Poletsky 型逆不等式的映射，证明其映射族的均匀边界为离散映射，并分别分析了边界局部连通区域与拟共形意义下正则区域的情形。
Carathéodory boundary extensions for generalized quasiregular mappings
研究了具有有界和有限扭曲的映射的边界行为，证明了在特定条件下，这些映射具有连续边界扩展，且结果适用于具有适当模条件的-homeomorphism和开放离散闭映射。
The article is devoted to mappings with bounded and finite distortion of plane domains. Our investigations are devoted to the connection between mappings of the Sobolev class and upper bounds for the distortion of the modulus of families of paths. For this class, we have proved the Poletsky-type inequality with respect to the so-called inner dilatation of the order~$p.$ Along the way, we also obtained lower bounds for the modulus distortion under mappings. We separately considered the situations of homeomorphisms and mappings with branch points.
On boundary non-preserving mappings with integral constraints
本文研究了满足特定积分约束的边界非保持映射，并证明了其在闭域上的等连续性。
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.
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。
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。
On Koebe's theorem for mappings with integral constraints
研究满足普洛特斯基型逆模数不等式的映射，证明某些球体的像包含固定球体，得出科贝定理的类比结果，并探讨Orlicz-Sobolev类映射的开放性和离散性。
Removable singularities of mappings with inverse Poletksy inequality on Rie\-man\-nian manifolds
本文研究Riemannian流形上满足逆Poletsky型模不等式的开离散映射，证明在遗漏至少两点且控制函数几乎处处球面可积时，边界孤立点为可去奇点。
We study global regularity properties of Sobolev homeomorphisms on $n$-dimensional Riemannian manifolds under the assumption of $p$-integrability of its first weak derivatives in degree $p\geq n-1$. We prove that inverse homeomorphisms have integrable first weak derivatives. For the case $p>n$ we obtain necessary conditions for existence of Sobolev homeomorphisms between manifolds. These necessary conditions based on Poincaré type inequality: $$ \inf_{c\in \mathbb R} \|u-c\mid L_{\infty}(M)\|\leq K \|u\mid L^1_{\infty}(M)\|. $$ As a corollary we obtain the following geometrical necessary condi…
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