Boundary behaviour of automorphisms of a hyperbolic spaceстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 6 февраля 2018 г.
Аннотация: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 Poincar´e’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, Poincar´e’s model, quasiconformal mapping,
equimorphism of the Lobachevsky space, asymptotic behaviour of the quasiconformality
coefficient, boundary behaviour of a mapping.