Liouville theorem on conformal mappings of domains in multidimensional Euclidean and Pseudoeuclidean spacesстатья
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Аннотация:Everybody who attended a course in complex analysis, knows Riemann Theorem on conformal mappings, demonstrating conformal flexibility of domains in the two-dimensional plane (more generally, in a two-dimensional surface). In contrast to the plane case, domains in spaces of dimension greater than two are conformally rigid. This is the content of a (less popular) Liouville theorem, which appeared almost in the same time as the mentioned Riemann theorem. Here we present one of the possible proofs of this theorem together with a contemporary bibliography containing new approaches to this theorem together with its generalizations and extensions.
Keywords: Quasiconformal mapping; conformal rigidity.
MSC: 30C65
ISSN 2406-0682 (Online), ISSN 0025–5165 (Print)
http://www.vesnik.math.rs/volumes.html#