A. Golberg

activity

20122025

collaborators

6 papers

math.CV2025

Modulus estimates of semirings with applications to boundary extension problems

Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen

In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $R^{n}$ with large enough modulus may be separated by an annular ring domain…

math.CV2020

Teichmüller's theorem in higher dimensions and its applications

Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen

For a given ring (domain) in $R^{n}$ we discuss whether its boundary components can be separated by an annular ring with modulus nearly equal to that of the given…

math.CV2018

Asymptotic dilation of regular homeomorphisms

Anatoly Golberg, Ruslan Salimov, Maria Stefanchuk

We study the asymptotic behavior of the ratio $∣ f (z) ∣/∣ z ∣$ as $z \to 0$ for mappings differentiable a.e. in the unit disc with non-degenerated Jacobian. The main tools involve the l…

math.CV2015

Absolute continuity on paths of spatial open discrete mappings

Anatoly Golberg, Evgeny Sevost'yanov

We prove that open discrete mappings of Sobolev classes $W_{loc}^{1, p},$ $p > n - 1,$ with locally integrable inner dilatations admit $A C P_{p}^{- 1}$ -property, which means that the…

math.CV2013

Equicontinuity and normality of mappings with integrally bounded $p$ -moduli

Anatoly Golberg, Ruslan Salimov, Evgeny Sevost'yanov

We consider the generic discrete open mappings in $R^{n}$ under which the perturbation of extremal lengths of curve collections is controlled integrally via $\int Q(x)η^p(|…

math.CV2012

Topological Mappings with Controlled $p$ -Moduli

Anatoly Golberg, Ruslan Salimov

We study homeomorphisms of controlled $p$ -module by certain integrals. In this way, we establish various properties of mappings and show that their features are close to quasiconfo…