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Information × Registration Number 0219U100072, 0118U100096 , R & D reports Title Geometric and analytic methods in the theory of mappings popup.stage_title Head Klishchuk Bogdan A., Кандидат фізико-математичних наук Registration Date 14-01-2019 Organization The Institute of Mathematics of NASU popup.description2  The object of the research is the problems of complex and hypercomplex analysis, the theory of mappings, and the theory of generalized convex sets. The aim of the work is to develop geometric and analytical methods of real, complex and hypercomplex analysis, to study the properties of mappings, to study extremal problems of the geometric theory of functions, and to find analytic-topological methods for solving problems of the theory of generalized convex sets. On the topic of work, there are established conditions on the complex Beltrami coefficient with degeneration in the unit circle under which generalized homeomorphic solutions are continuous by Gelder on the boundary. There are obtained lower bounds for the image of the ball for homeomorphic mappings with respect to a nonconformal module in the many-valued Euclidean space. Sharp estimates of products of inner radii of nonoverlapping domain in the complex plane are obtained. Properties of generalized convex sets and mappings in the real and hypercomplex spaces are investigated. The results obtained can be applied in the theory of functions, potential theory, the theory of mappings, the theory of systems of nonlinear differential equations, the theory of boundary value problems, which, in turn, find application in hydrodynamics, thermal physics, mechanics, theoretical physics, tomography and other scientific disciplines. Product Description popup.authors popup.nrat_date 2020-04-02 Close