Study of boundary behavior of mappings in metric spaces and their generalization

Work number - M 73 ALLOWED TO PARTICIPATE

Presented by the Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine

Author: Afanaseva E.S.

The paper is devoted to the boundary behavior of mappings with finite distortion in metric spaces, Riemannian and Finsler manifolds. The study provides a basis for solving boundary value problems of Beltrami equations with violation of the strict ellipticity condition. A number of fundamental criteria have been obtained that establish a connection between mappings. They are important from the point of view of applications (for arbitrary diffeomorphisms, finite bi-Lipschitz mappings, isometries, and quasi-isometries). The formulation of new non-traditional problems for obtaining an integral condition sufficient and necessary for continuous extension to the boundary of mappings in metric spaces with measures was carried out. The results of the cycle are important for investigating the boundary behavior of mappings in many known regular domains (smooth, Lipschitz, uniform, quasi -extremal length by Gehring -Martio, etc.).

The obtained results have a theoretical value and a significant contribution to the theory of functions. It could be interested to scientists from related fields and could be used for further research in the IM NAS of Ukraine (Kiev), IAMM NAS of Ukraine (Slavyansk), the Institute of Mathematics of the Polish Academy of Sciences (Warsaw), the Institute of Mathematics of the Romanian Academy of Sciences (Bucharest), the Institute of Mathematics of the SB of the RAS, Technion (Haifa, Israel), the Institute of Technology (Holon, Israel), Helsinki (Finland) and Michigan (USA) universities.

Publications: 37, including 25 articles (8 – in foreign publications, 17 – in leading Ukrainian publications). According to the Scopus database, the total number of links to the author's publications (taking into account the surname before marriage (Smolovaya), under which the articles included in this series of works came out) is 20, the h-index (by work) = 2; according to the Google Scholar database, the total number of links is 32, the h-index (by work) = 3.

On this subject the author defended PhD thesis. The results of the work were reported at many international scientific conferences and discussed in leading Ukrainian and foreign scientific institutions.