Isometries of the quasihyperbolic metric

Peter Hästö

Vol. 230 (2007), No. 2, 315–326

DOI: 10.2140/pjm.2007.230.315

Abstract

We study the curvature and isometries of the quasihyperbolic metric on plane domains. We prove that, except for the trivial case of a half-plane, the isometries are exactly the similarity mappings. We need to assume that the boundary of the domain is C³ smooth.

Keywords

quasihyperbolic metric, isometries, Gaussian curvature

Mathematical Subject Classification 2000

Primary: 30F45

Milestones

Received: 26 August 2005

Accepted: 22 August 2006

Published: 1 April 2007