Real, complex and functional analysis

Rectangle as a generalized angle

V. V. Aseev

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

Abstract: In order to extend the notion of quasimöbius mapping to non-injective case the concept of generalized angle $\Psi = (A_1, A_2; B_1, B_2)$ with sides $A_1, A_2$ and vertices $B_1, B_2$ (the sets in a Ptolemaic space) has been employed. The value of a generalizes angle is defined through Ptolimaic characteristic of tetrads and is not easy to by calculated in general case. Here we present the geometric way of calculation in the case where the general angle $\Psi$ is a rectangle.

Keywords: quasimöbius mapping, quasiregular mapping, Ptolemaic space, generalized angle, mapping of bounded angular distortion, set-valued mapping.

UDC: 517.54

MSC: 30C65

Received April 2, 2019, published December 26, 2019

Language: English

DOI: 10.33048/semi.2019.16.144

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