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Isometries of the quasihyperbolic metric

Peter Hästö
2007 Pacific Journal of Mathematics  
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 C 3 smooth. MSC2000: 30F45.
doi:10.2140/pjm.2007.230.315 fatcat:esbb2i52evguzapnkgyz7pr63m