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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 5, Pages 976–987
DOI: https://doi.org/10.17377/smzh.2018.59.503 (Mi smj3023) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Generalized angles in Ptolemaic Möbius structures. II

V. V. Aseev

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (311 kB) Citations (12)
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DOI: https://doi.org/10.17377/smzh.2018.59.503
Abstract: We continue studying the BAD class of multivalued mappings of Ptolemaic Möbius structures in the sense of Buyalo with controlled distortion of generalized angles. In Möbius structures we introduce a Möbius-invariant version of the HTB property (homogeneous total boundedness) of metric spaces which is qualitatively equivalent to the doubling property. We show that in the presence of this property and the uniform perfectness property, a single-valued mapping is of the BAD class iff it is quasimöbius.
Keywords: Möbius structure, Ptolemaic space, quasimöbius mapping, quasisymmetric mapping, inversion metric, inversion space, uniformly perfect space, HTB-space.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 1.1.2, 0314-2016-0007
The author was supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant 1.1.2, Project 0314-2016-0007).
Received: 22.12.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 5, Pages 768–777
DOI: https://doi.org/10.1134/S0037446618050038
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 35R30
Language: Russian
Citation: V. V. Aseev, “Generalized angles in Ptolemaic Möbius structures. II”, Sibirsk. Mat. Zh., 59:5 (2018), 976–987; Siberian Math. J., 59:5 (2018), 768–777
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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