Registration Number
0126U003569,
R & D request
Title
Analogues of Carathéodory and Koebe-Bloch theorems for
Orlycz-Sobolev classes
Head
Yevhen O. Sevostianov, д.ф.-м.н.
Registration Date
22-04-2026
Organization
Zhytomyr Ivan Franko State University
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In general, the goal of the project is to create scientific results (theorems) that will adequately
represent scientific research in Ukraine on the international stage, in particular, it is planned to
publish these results in top scientific journals. It is planned to write at least two PhD dissertations,
create university special courses for masters, etc. Among other things, the goal of the project is:
1) development of the theory of mappings, in particular, development of local and boundary
behavior of mappings, development of modulus techniques, development of the theory of prime
ends, development of the theory of metric spaces; 2) obtaining analogues of the Carathéodory
theorem on continuous extension in terms of prime ends of mappings of Sobolev and OrlyczSobolev classes that do not preserve the boundary of the domain; 3) obtaining analogues of the
Koebe-Bloch theorems on the radius of a ball for one class of spatial open discrete mappings
which contains itself inverses homeomorphisms of Orlycz-Sobolev; 4) the generalization of the
above results to some metric spaces (Riemannian manifolds, surfaces, factor spaces over the
group of Möbius mappings of the unit ball that act discontinuously without fixed points, etc.)
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2026-04-22
