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Iurii
Zelinskyi
Professor Iurii Zelinskyi was born in 1947-02-22 in Borschiv, Ternopil region of Ukraine.
1973 - PhD Institute of mathematics Ukrainian Academy of Science.
Sciences biography. 1965 – 1970 – student of mechanical and mathematical faculty of Kyiv University. 1970 – 1973 – post-graduate student of Institute of mathematics Ukrainian Academy of Science. From 1973 till now he works in the Institute of Mathematics of NASU (from 2003 he works as a head of department of complex analysis and potential theory).
The circle of scientific interests: application of topological and geometrical methods in analytical problems of complex analysis and theory of mappings.
The
main scientific results.
Theory
of mappings: He is the first
who applied local degree of mapping to multivalued mappings of topological
manifolds. Thanks to this it is solved the problem of estimation dimensionality
of subset with fixed multiplicity for the mappings of domains on the manifolds
if the properties of mappings on the boundary of domains are known. Those open
problems where proposed by polish mathematicians H Steinhaus and A.Kosiński
in 50-th of the last century.
Complex analysis: He generalized the principle of the boundary correspondence to mappings between domains of n-dimensional complex manifolds, obtaining from minimal conditions on the boundary results concerning univalence or monotony of mappings, singularities elimination.
He applied geometrical methods and method of multivalued mapping to analytical problems. He deeply studied the relations between different types of convexity and obtained the full topological classification of linearly convex and strongly convex sets with smooth boundaries; he received estimates 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. He created a new direction in complex analysis which is analog of classical real convex analysis. Using his own methods, he proposed a new approach in the research of generalized convex sets on the Grassmanian manifolds.
He is the author of more then 220 scientific works among which there are three monographs and 14 educational supplies.
Language knowledge: English, French, Polish, Esperanto
Selected publications.
1. Zelīnskiĭ, Ju. B. Certain problems of A. Kosiński. Ukrain. Mat. Ž. 27 (1975), no. 4, 510--516, (in Russian).
2. Zelinski Yu. On connection between properties of a compact set in Cn and its conjugate set. Lecture Notes Math. № 798, Springer 1980.-p. 465-476.
3. Zelinskiĭ, Yu. B. On linearly convex domains with smooth boundaries. Ukrainian Math. J. 40 (1988), no. 1, 44--48
4. Zelinski Yu. Derivatives in the direction and subdifferentials of linearly convex functions. Pitman Research Notes in Math. Ser. № 257, 1991.- р.118-122
5. Zelinski Yu. Multivalued mappings in analysis.- Kyiv; Naukova dumka .-1993.- 264 p.(in Russian)
6. Zelinskiĭ, Yu. B. The Helly theorem and related results. Ukrainian Math. J. 54 (2002), no. 1, 149--153
7. Bahtin A.K., Bahtina G.P., Zelinskii Y.B.. Topologic-algebraic structures and geometric methods in complex analysis. Kyiv; Institute of mathematics.- 2008.- 308 p. .(in Russian)