- Institute of mathematics NASU
Tereshchenkivska str.3
Kyiv Ukraine - 234-53-03
Yuri Zelinski
Institute of mathematics NASU, Kyiv, Complex analysis, Faculty Member
The monograph is devoted to the development of geometric and topological methods of analysis and study with them linearly convex sets and fixed points sets. Much attention is paid to the development of a new method of research for... more
The monograph is devoted to the development of geometric and topological methods of analysis and study with them linearly convex sets and fixed points sets.
Much attention is paid to the development of a new method of research for linearly convex sets in complex spaces, based on the studying graphs of multi-valued maps. The relations between different types of convexity is studied and obtained the full topological classification of linearly convex and strongly convex sets with smooth boundaries. We estimate of cohomology groups for generalized convex domains and compacts in multidimensional complex space. In this connection, well known problems of L. Aizenberg of description of generalized convex sets are solved. Also
Is given a number of complex analogues of classical theorems (Hahn-Banach,
Krein-Milman, Caratheodory, Fenchel-Moreau).
Much attention is paid to the development of a new method of research for linearly convex sets in complex spaces, based on the studying graphs of multi-valued maps. The relations between different types of convexity is studied and obtained the full topological classification of linearly convex and strongly convex sets with smooth boundaries. We estimate of cohomology groups for generalized convex domains and compacts in multidimensional complex space. In this connection, well known problems of L. Aizenberg of description of generalized convex sets are solved. Also
Is given a number of complex analogues of classical theorems (Hahn-Banach,
Krein-Milman, Caratheodory, Fenchel-Moreau).
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In this lecture we consider the results on building generalized convex hull for family consisting of convex sets in real and (hyper)complex Euclidean space. The unsolved questions related to those problems were discussed.
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In this review we consider the results on building generalized convex hull for family consisting of convex sets in real and (hyper)complex Euclidean space. The unsolved questions related to those problems are discussed.
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В работе рассмотрим связь между инволюциями на замкнутом многообразии и отображениями таких многообразий, каждая точка образа которых содержит не более двух прообразов. We investigate possibility of the building on manifold continuous... more
В работе рассмотрим связь между инволюциями на замкнутом многообразии и отображениями таких многообразий, каждая точка образа которых содержит не более двух прообразов.
We investigate possibility of the building on manifold continuous involution and connected with her continuous mapping for which each point of the image has not more than two preimages.
We investigate possibility of the building on manifold continuous involution and connected with her continuous mapping for which each point of the image has not more than two preimages.
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Les auteurs montrent pour les polyèdres linéaires un théorème du type Krein-Milman.
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The subject, which is treated in this report, combines in one bundle some questions of complex analysis, geometry and probability theory. Our purpose is to give a review of open problems and known results. First investigations in... more
The subject, which is treated in this report, combines in one bundle some questions of complex analysis, geometry and probability theory. Our purpose is to give a review of open problems and known results. First investigations in geometric probability theory start from the well known Buffoons needle problem and related Bertrand paradoxes. Further, the paper introduces original conjectures and results of the present author. See also the author’s paper in [ibid. 60, No. 3, 73–80 (2010; Zbl 1241.52005)].
Some questions of integral complex geometry. Available from: https://www.researchgate.net/publication/268543293_Some_questions_of_integral_complex_geometry [accessed Jun 6, 2015].
Some questions of integral complex geometry. Available from: https://www.researchgate.net/publication/268543293_Some_questions_of_integral_complex_geometry [accessed Jun 6, 2015].
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The purpose of this lecture - pay attention to some interesting unsolved problems, which are often formulated very simply, but the solution of which, according to the author's conversations with experts from complex analysis and topology,... more
The purpose of this lecture - pay attention to some interesting unsolved problems, which are often formulated very simply, but the solution of which, according to the author's conversations with experts from complex analysis and topology, requiring, perhaps, fresh ideas.