13 citations · 19 across the 9 of their papers we have counts for
16 papers
Hulls and boundaries in
Stefan Nemirovski, Josias Reppekus, Nikolay Shcherbina
The paper is concerned with the boundary behaviour of polynomially and rationally convex hulls in pseudoconvex domains in . As an application, it is shown that every…
On compact sets possessing -convex functions
Thomas Pawlaschyk, Nikolay Shcherbina
We show that there exists a -convex function in a neighborhood of a compact set in a complex manifold if and only if the -nucleus of this compact set is emp…
Topological invariants and Holomorphic Mappings
Robert E. Greene, Kang-Tae Kim, Nikolay V. Shcherbina
Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of…
On compacts possessing strictly plurisubharmonic functions
Nikolay Shcherbina
We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined i…
Foliations of continuous q-pseudoconcave graphs
Thomas Pawlaschyk, Nikolay Shcherbina
We show that for the graph of a continuous mapping , defined on a domain in , is locally foli…
A Kobayashi and Bergman complete domain without bounded representations
Nikolay Shcherbina, Liyou Zhang
We construct an unbounded strictly pseudoconvex Kobayashi hyperbolic and complete domain in , which also possesses complete Bergman metric, but has no nonconstant bou…
Unbounded Kobayashi hyperbolic domains in
Hervé Gaussier, Nikolay Shcherbina
We first give a sufficient condition, issued from pluripotential theory, for an unbounded domain in the complex Euclidean space to be Kobayashi hyperbolic. Then, we c…
On the existence of Kobayashi and Bergman metrics for Model domains
Nikolay Shcherbina
We prove that for a pseudoconvex domain of the form , where and F is a continuous function on ${\mathbb C}_z \…
Plurisubharmonically separable complex manifolds
Evgeny A. Poletsky, Nikolay Shcherbina
Let be a complex manifold and be the space of bounded continuous plurisubharmonic functions on . In this paper we study when functions from separ…
Squeezing functions and Cantor Sets
Leandro Arosio, John Erik Fornæss, Nikolay Shcherbina +1
We construct "large" Cantor sets whose complements resemble the unit disk arbitrarily well from the point of view of the squeezing function, and we construct "large" Cantor sets wh…
A domain with non-plurisubharmonic squeezing function
John Erik Fornæss, Nikolay Shcherbina
We construct a strictly pseudoconvex domain with smooth boundary whose squeezing function is not plurisubharmonic.
The Hartogs Extension Theorem for holomorphic vector bundles and sprays
Rafael B. Andrist, Nikolay Shcherbina, Erlend F. Wold
We study ellipticity properties of complements of compact subsets of Stein manifolds.
On defining functions for unbounded pseudoconvex domains
Tobias Harz, Nikolay Shcherbina, Giuseppe Tomassini
We show that every strictly pseudoconvex domain with smooth boundary in a complex manifold admits a global defining function, i.e., a smooth plurisubharmonic func…
Wermer type sets and extension of CR functions
Tobias Harz, Nikolay Shcherbina, Giuseppe Tomassini
For each we construct an unbounded closed pseudoconcave complete pluripolar set in which contains no analytic variety of positive dimension (we…
On the set of complex points of a 2-sphere
Nikolay Shcherbina
Let be a strictly pseudoconvex domain in with -smooth boundary . Let be a 2-dimensional sphere embedded into . Denote by $\…
Pluripolar graphs are holomorphic
N. V. Shcherbina
We prove that the graph of a continuous function , defined on a domain of , is pluripolar if and only if is holomorphic.