Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Shcherbina Nikolay"'
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 closed curves and maps of the $k$-sphere into the manifold are investi
Externí odkaz:
http://arxiv.org/abs/2107.14393
Autor:
Shcherbina, Nikolay
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 in a neighbourhood of this set.
Comment: 15 pages. Comments welcom
Comment: 15 pages. Comments welcom
Externí odkaz:
http://arxiv.org/abs/2004.14469
We show that for $k = 0, 1$ the graph of a continuous mapping $f:D \to \mathbb{R}^k\times\mathbb{C}^p$, defined on a domain $D$ in $\mathbb{C}^n\times\mathbb{R}^k$, is locally foliated by complex $n$-dimensional submanifolds if and only if its comple
Externí odkaz:
http://arxiv.org/abs/2004.01797
Autor:
Shcherbina, Nikolay, Zhang, Liyou
We construct an unbounded strictly pseudoconvex Kobayashi hyperbolic and complete domain in $\mathbb{C}^2$, which also possesses complete Bergman metric, but has no nonconstant bounded holomorphic functions.
Comment: 15 pages. Comments welcome!
Comment: 15 pages. Comments welcome!
Externí odkaz:
http://arxiv.org/abs/2003.06728
Autor:
Gaussier, Hervé, Shcherbina, Nikolay
We first give a sufficient condition, issued from pluripotential theory, for an unbounded domain in the complex Euclidean space $\mathbb C^n$ to be Kobayashi hyperbolic. Then, we construct an example of a rigid pseudoconvex domain in $\mathbb C^3$ th
Externí odkaz:
http://arxiv.org/abs/1911.05632
Autor:
Shcherbina, Nikolay
We prove that for a pseudoconvex domain of the form $\mathfrak{A} = \{(z, w) \in \mathbb C^2 : v > F(z, u)\}$, where $w = u + iv$ and F is a continuous function on ${\mathbb C}_z \times {\mathbb R}_u$, the following conditions are equivalent: (1) The
Externí odkaz:
http://arxiv.org/abs/1904.12950
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G8, Pp 829-844 (2022)
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 closed curves and maps of the $k$-sphere into the manifold are investi
Externí odkaz:
https://doaj.org/article/88ef8a1d940d45f5a94ebdf163fe82ee
Let $M$ be a complex manifold and $PSH^{cb}(M)$ be the space of bounded continuous plurisubharmonic functions on $M$. In this paper we study when functions from $PSH^{cb}(M)$ separate points. Our main results show that this property is equivalent to
Externí odkaz:
http://arxiv.org/abs/1712.02005
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 whose complements do not resemble the unit disk from the point of view o
Externí odkaz:
http://arxiv.org/abs/1710.10305
We construct a strictly pseudoconvex domain with smooth boundary whose squeezing function is not plurisubharmonic.
Comment: 9 pages, 4 figures
Comment: 9 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/1604.01480