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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 2, Pages 241–256
DOI: https://doi.org/10.17377/smzh.2018.59.201 (Mi smj2968) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Generalized angles in Ptolemaic Möbius structures

V. V. Aseev

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (357 kB) Citations (16)
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DOI: https://doi.org/10.17377/smzh.2018.59.201
Abstract: We show that each Ptolemaic semimetric is Möbius-equivalent to a bounded metric. Introducing generalized angles in Ptolemaic Möbius structures, we study the class of multivalued mappings $F\colon X\to2^Y$ with a lower bound on the distortion of generalized angles. We prove that the inverse mapping to the coordinate function of a quasimeromorphic automorphism of $\overline{\mathbb R}^n$ lies in this class.
Keywords: Möbius structure, Ptolemy's inequality, Ptolemaic semimetric, angular metric, Möbius-invariant metric, quasimöbius mapping, generalized angle, quasimeromorphic mapping.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 1.1.2, проект 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 No. 1.1.2, Project 0314-2016-0007).
Received: 14.07.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 2, Pages 189–201
DOI: https://doi.org/10.1134/S0037446618020015
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 35R30
Language: Russian
Citation: V. V. Aseev, “Generalized angles in Ptolemaic Möbius structures”, Sibirsk. Mat. Zh., 59:2 (2018), 241–256; Siberian Math. J., 59:2 (2018), 189–201
Citation in format AMSBIB
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    This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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