20 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Bulgarian Academy of SciencesBG23 papers
- Institute of Mathematics and InformaticsBG21 papers
- Institut de Mathématiques de ToulouseFR8 papers
- Université Toulouse III - Paul SabatierFR8 papers
- Centre National de la Recherche ScientifiqueFR7 papers
- Université de ToulouseFR6 papers
- Jagiellonian UniversityPL5 papers
- Université Fédérale de Toulouse Midi-PyrénéesFR4 papers
- Institute of Information and Communication TechnologiesBG3 papers
- Toulouse Mathematics Institute3 papers
- Adam Mickiewicz University in PoznańPL2 papers
- Indian Institute of Science BangaloreIN2 papers
22 papers · 1 filter
A Picard little theorem for entire functions of matrices
Oleg Mushkarov, Nikolai Nikolov
An analog of Picard's little theorem for entire functions of matrices is proved.
Explicit universal bounds for squeezing functions of (-)convex domains
Gautam Bharali, Nikolai Nikolov
We prove two separate lower bounds -- one for nondegenerate convex domains and the other for nondegenerate -convex (but not necessarily convex) domains -- for the squee…
A Gehring-Hayman inequality for strongly pseudoconvex domains
Łukasz Kosiński, Nikolai Nikolov, Pascal J. Thomas
We prove that in a strongly pseudoconvex domain with smooth boundary, then the length of a geodesic for the Kobayashi-Royden infinitesimal metric between two points is bounded by a…
Strong localizations of the Kobayashi distance
Nikolai Nikolov, Ahmed Yekta Ökten
Recently, the visibility property of Kobayashi (almost) geodesics has been used to provide localizations of the Kobayashi distance. In this note, we provide sufficient growth condi…
Local and global notions of visibility with respect to Kobayashi distance, a comparison
Nikolai Nikolov, Ahmed Yekta Ökten, Pascal J. Thomas
In this note, we introduce the notion of visible boundary points with respect to Kobayashi distance for domains in complex euclidean space. Following the work of Sarkar, we obtain…
Lower estimates of the Kobayashi distance and limits of complex geodesics
Łukasz Kosiński, Nikolai Nikolov
It is proved for a strongly pseudoconvex domain in with -smooth boundary that any complex geodesic through every two close points of sufficient…
Strongly Goldilocks Domains, quantitative Visibility, and Applications
Nikolai Nikolov, Ahmed Yekta Ökten
In the last decade, G. Bharali and A. Zimmer defined a class of domains called Goldilocks domains and they showed that such a domain satisfies a visibility condition with respect t…
Growth of Sibony metric and Bergman kernel for domains with low regularity
Nikolai Nikolov, Pascal J. Thomas
It is shown that even a weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with boundary: the product of the Bergman kernel by the…
An analogue of the squeezing function for projective maps
Nikolai Nikolov, Pascal J. Thomas
In the spirit of Kobayashi's applications of methods of invariant metrics to questions of projective geometry, we introduce a projective analogue of the complex squeezing function.…
Comparison of the Bergman kernel and the Carathéodory--Eisenman volume
Nikolai Nikolov, Pascal J. Thomas
It is proved that for any domain in the Caratheodory--Eisenman volume is comparable with the volume of the indicatrix of the Caratheodory metric up to small/large con…
On the squeezing function and Fridman invariants
Nikolai Nikolov, Kaushal Verma
For a domain , the relationship between the squeezing function and the Fridman invariants is clarified. Furthermore, localization properties of these functio…
Estimates for the squeezing function near strictly pseudoconvex boundary points with applications
Nikolai Nikolov, Maria Trybuła
An extension of the estimates for the squeezing function of strictly pseudoconvex domains obtained recently by J. E. Fornæss and E. Wold in \cite{FW1} is applied to derive a sharp…
Behavior of the squeezing function near h-extendible boundary points
Nikolai Nikolov
It is shown that if the squeezing function tends to one at an h-extendible boundary point of a -smooth, bounded pseudoconvex domain, then the point is strictly p…
Boundary behavior of the squeezing functions of -convex domains and plane domains
Nikolai Nikolov, Lyubomir Andreev
It is shown that any non-degenerate -convex domain in is uniformly squeezing. It is also found the precise behavior of the squeezing function near a Dini-s…
On a lower bound of the Kobayashi metric
Nikolai Nikolov
It is shown that a lower bound of the Kobayashi metric of convex domains in C^n does not hold for non-convex domains.
Boundary behavior of invariant functions on planar domains
Nikolai Nikolov, Maria Trybula, Lyubomir Andreev
Precise behavior of the Caratheodory, Kobayashi and Bergman metrics and distances near smooth boundary points of domains in C is found under different assumptions of regularity.
Estimates of the Kobayashi and quasi-hyperbolic distances
Nikolai Nikolov, Lyubomir Andreev
Universal upper bounds for the Kobayashi and quasi-hyperbolic distances near Dini-smooth boundary points of domains in $\C^n$ and respectively, are obtained.
Two remarks on the Suita conjecture
Nikolai Nikolov
It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with -smooth boundary. On the other hand, it is prove…
Estimates of the Bergman distance on Dini-smooth bounded planar domains
Nikolai Nikolov, Maria Trybuła
Precise estimates for the Bergman distances of Dini-smooth bounded planar domains are given. These estimates imply that on such domains the Bergman distance almost coincides with t…
The Kobayashi balls of C-convex domains
Nikolai Nikolov, Maria Trybula
A pure geometric description of the Kobayashi balls of C-convex domains is given in terms of the so-called minimal basis.
Gromov (non)hyperbolicity of certain domains in
Nikolai Nikolov, Pascal J. Thomas, Maria Trybula
We prove the non-hyperbolicity of the Kobayashi distance for -smooth convex domains in which contain an analytic disc in the boundary or have a…
Estimates of invariant distances on "convex" domains
Nikolai Nikolov
Estimates for invariant distances of convexifiable, $\C$-convexifiable and planar domains are given.