V. V. Aseev, “Generalized angles in Ptolemaic Möbius structures. II”, Sibirsk. Mat. Zh., 2018, Volume 59, Number 5,Pages <nobr>976

This article is cited in 10 papers

Generalized angles in Ptolemaic Möbius structures. II

V. V. Aseev

Sobolev Institute of Mathematics, Novosibirsk, Russia

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.

UDC: 517.54

MSC: 35R30

Received: 22.12.2017

DOI: 10.17377/smzh.2018.59.503