MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Liouville theorem on conformal mappings of domains in multidimensional Euclidean and Pseudoeuclidean spaces
V. A. Zorich

Abstract

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.

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Keywords: Quasiconformal mapping; conformal rigidity.

MSC: 30C65

Pages:  183$-$188     

Volume  70 ,  Issue  2 ,  2018