Vol. 230, No. 2, 2007

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Isometries of the quasihyperbolic metric

Peter Hästö

Vol. 230 (2007), No. 2, 315–326
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
Authors
Peter Hästö
Department of Mathematical Sciences
P.O. Box 3000
FI-90014 University of Oulu
Finland
http://cc.oulu.fi/~phasto