Work

The purpose of the proposed research work is to conduct research on a wide range of current issues of modern real and complex analysis, with emphasis on the latest trends and approaches in these areas of mathematics. The focus will be on the research in the following areas: development of complex analysis, theory of analytical functions, theory of conformal mappings and their generalizations, extremal problems of theory of analytic functions, development of variational, symmetrization, extreme-metric methods of analysis and their application to geometric and constructive theory of functions, extremization of functionals defined on the main classes of univalent functions and families of mappings. The expected results can be used in function theory, potential theory, mapping theory, systems theory of nonlinear differential equations, theory of boundary value problems, which, in turn, are used in hydrodynamics, gas dynamics, thermophysics, mechanics, theoretical physics, tomography and other scientific disciplines.