PhD of Sciences (Physics and Mathematics)
Institute of Mathematics of the National Academy of Sciences of Ukraine,
Tereshchenkivska Str. 3, 01601, Kiev, Ukraine
Phone (office): (38044) 234–51–50
Address: Tchornobylska Str., 4/56, apt. 70, Kiev 03179, Ukraine
– student of Kiev Taras Shevchenko State University, Faculty of Physics and Mathematics;
– post-graduate student at the Institute of Mathematics of the Ukrainian Academy of Sciences and PhD thesis under the guidance of Professor Alexander Bahtin;
– from 2010 she works at the Complex Analysis and the Potential Theory Department of the Institute of Mathematics of NASU as junior researcher.
The circle of scientific interests. Generalized convex sets on Grassmann manifolds (partly in Euclidean real, complex spaces and hypercomplex spaces) and its applications.
The main scientific results. The classical Caratheodory theorem for bounded and unbounded sets in the case when the original set consists of a limited number of components or sections of a set by planes of fixed dimension contain a limited number of components is generalized. The new external and boundary criteria for convexity domains and compact sets in Euclidean space are established. It is shown that the convexity of domain in Euclidean space can be received from some characteristics of the complement of this domain, or from crossing properties of conjugate to this domain compact by supporting planes. For acyclic compacts boundary criterion of strong linear convexity is founded. Criterion for strong linear convexity Cartesian product of compacts in multidimensional hypercomplex space is established. Those results greatly enhanced the known results of G.Aumann , A.Kosinski , E.Schepin, Yu.Zelinskii in the case of a priori acyclic sets.