The visual angle metric and Möbius transformations - UTU Research Portal

A1 Refereed original research article in a scientific journal

The visual angle metric and Möbius transformations

Authors: Riku Klén, Henri Lindén, Matti Vuorinen, Gendi Wang

Publisher: SPRINGER HEIDELBERG

Publishing place: HEIDELBERG; TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY

Publication year: 2014

Journal: Computational Methods and Function Theory

Journal name in source: Computational Methods and Function Theory

Journal acronym: Comput.Methods Funct.Theory

Volume: 14

Issue: 2-3

First page : 577

Last page: 608

Number of pages: 32

ISSN: 1617-9447

DOI: https://doi.org/10.1007/s40315-014-0075-x

Abstract

A new similarity invariant metric is introduced. The visual angle metric is defined on a domain whose boundary is not a proper subset of a line. We find sharp bounds for in terms of the hyperbolic metric in the particular case when the domain is either the unit ball or the upper half space . We also obtain the sharp Lipschitz constant for a Mobius transformation between domains and in with respect to the metrics and . For instance, in the case the result is sharp.