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Russian Mathematical Surveys, 2017, Volume 72, Issue 4, Pages 645–670
DOI: https://doi.org/10.1070/RM9785 (Mi rm9785) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Boundary behaviour of automorphisms of a hyperbolic space

V. A. Zorich

Moscow State University
English version PDF (554 kB) Citations (2)
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DOI: https://doi.org/10.1070/RM9785
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.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00592-а
Ministry of Education and Science of the Russian Federation НШ-9110.2016.1
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 17-01-00592-a) and the programme “Leading Scientific Schools” (grant no. НШ-9110.2016.1).
Received: 20.06.2017
Russian version:
Uspekhi Matematicheskikh Nauk, 2017, Volume 72, Issue 4(436), Pages 67–94
DOI: https://doi.org/10.4213/rm9785
Bibliographic databases:
Document Type: Article
UDC: 517.54+514.774
MSC: Primary 30C62, 30C65; Secondary 51M10
Language: English
Original paper language: Russian
Citation: V. A. Zorich, “Boundary behaviour of automorphisms of a hyperbolic space”, Uspekhi Mat. Nauk, 72:4(436) (2017), 67–94; Russian Math. Surveys, 72:4 (2017), 645–670
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    Abstract page:1247
    Russian version PDF:80
    English version PDF:22
    References:48
    First page:38
     
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