6 papers · 1 filter
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…
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 \…
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.