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

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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

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Linking options:

https://www.mathnet.ru/eng/smj3023

https://www.mathnet.ru/eng/smj/v59/i5/p976

Cycle of papers

Generalized angles in Ptolemaic Möbius structures
V. V. Aseev
Sibirsk. Mat. Zh., 2018, 59:2, 241–256
Generalized angles in Ptolemaic Möbius structures. II
V. V. Aseev
Sibirsk. Mat. Zh., 2018, 59:5, 976–987

This publication is cited in the following 12 articles:

V. V. Aseev, “The Ptolemaic Characteristic of Tetrads and Quasiregular Mappings”, Sib Math J, 65:5 (2024), 995
V. V. Aseev, “Ptolemeeva kharakteristika tetrad i kvaziregulyarnye otobrazheniya”, Sib. matem. zhurn., 65:5 (2024), 785–794
V. V. Aseev, “Mnogoznachnye kvazimëbiusovy otobrazheniya na rimanovoi sfere”, Sib. matem. zhurn., 64:3 (2023), 450–464
N. V. Abrosimov, V. V. Aseev, “Multivalued quasimöbius property and bounded turning”, Sib. elektron. matem. izv., 20:2 (2023), 1185–1199
V. V. Aseev, “The Multi-Valued Quasimöbius Mappings on the Riemann Sphere”, Sib Math J, 64:3 (2023), 514
Zhiqiang Yang, Qingshan Zhou, “Topological Angles and Freely Quasiconformal Mappings in Real Banach Spaces”, Comput. Methods Funct. Theory, 23:2 (2023), 347
V. V. Aseev, “Bounded turning in Möbius structures”, Siberian Math. J., 63:5 (2022), 819–833
V. V. Aseev, “Multivalued quasimöbius mappings from circle to circle”, Siberian Math. J., 62:1 (2021), 14–22
V. V. Aseev, “Adherence of the images of points under multivalued quasimöbius mappings”, Siberian Math. J., 61:3 (2020), 391–402
Q. Zhou, Ya. Li, A. Xiao, “On uniform perfectness in quasimetric spaces”, Filomat, 34:6 (2020), 1975–1987
V. V. Aseev, “Rectangle as a generalized angle”, Sib. elektron. matem. izv., 16 (2019), 2013–2018
V. V. Aseev, “Multivalued mappings with the quasimöbius property”, Siberian Math. J., 60:5 (2019), 741–756

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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