Abstract:
An automorphism of a Euclidean ball extends to a homeomorphic mapping of the closed ball even when the quasiconformality coefficient of the mapping increases unboundedly but in a controlled way upon approaching the boundary of the ball.
By means of Poincaré's conformally Euclidean model of the Lobachevsky space, this yields a condition under which an automorphism of a hyperbolic space still extends to the ideal boundary (the absolute) of the space when translated into geometric language.
Bibliography: 28 titles.
Keywords:hyperbolic space, Poincaré's model, quasiconformal mapping, equimorphism of the Lobachevsky space, asymptotic behaviour of the quasiconformality coefficient, boundary behaviour of a mapping.
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