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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 246–257 (Mi semr914)  

Real, complex and functional analysis

The coefficient of quasimöbiusness in Ptolemaic spaces

V. V. Aseev

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: In ptolemaic spaces the class of $\eta$-quasimöbius mappings $f: X\to Y$ with control function $\eta(t)= C \max\{ t^{\alpha}, t^{1/\alpha}\}$ may be completely characterized by the inequality $ K^{-1}\leq (1 + \log P(fT))/(1+ \log P(T)) \leq K$ for all tetrads $T\subset X$ where $P(T)$ denotes the ptolemaic characteristic of a tetrad. The number $K$ has properties quite similar to those of coefficients of quasiconformality, so the concept of $K$-quasimöbius mapping may be introduced. In particular, the stability theorem is proved for $(1+\varepsilon)$-quasimöbius mappings in $\bar{R}^n$.

Keywords: ptolemaic space, Möbius mapping, quasimöbius mapping, (power) quasimöbius mapping, quasisymmetric mapping, stability theorem.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 1.1.2, project No. 0314-2016-0007
The work is supported by the program of fundamental scientific researches of the SB RAS No. 1.1.2., project No. 0314-2016-0007.


DOI: https://doi.org/10.17377/semi.2018.15.023

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Bibliographic databases:

Document Type: Article
UDC: 517.54
MSC: 30C65
Received June 28, 2017, published March 16, 2018
Language: English

Citation: V. V. Aseev, “The coefficient of quasimöbiusness in Ptolemaic spaces”, Sib. Èlektron. Mat. Izv., 15 (2018), 246–257

Citation in format AMSBIB
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\by V.~V.~Aseev
\paper The coefficient of quasim\"obiusness in Ptolemaic spaces
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 246--257
\mathnet{http://mi.mathnet.ru/semr914}
\crossref{https://doi.org/10.17377/semi.2018.15.023}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200023}


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