On Isometries of Conformally Invariant Metrics - UTU Research Portal

A1 Refereed original research article in a scientific journal

On Isometries of Conformally Invariant Metrics

Authors: Riku Klén, Matti Vuorinen, Xiaohui Zhang

Publisher: SPRINGER

Publication year: 2016

Journal: Journal of Geometric Analysis

Volume: 26

Issue: 2

First page : 914

Last page: 923

Number of pages: 10

ISSN: 1050-6926

eISSN: 1559-002X

DOI: https://doi.org/10.1007/s12220-015-9577-7

Abstract

We prove that isometries in a conformally invariant metric of a general domain are quasiconformal. In the particular case of the punctured space, we prove that isometries in this metric are Möbius, thus resolving a conjecture of Ferrand et al. (J Anal Math 56: 187–120, 1991) in this particular case.