Acta mathematica scientia,Series A

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Apollonian Isometries and Mobius Transformations

Chu Yuming   

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000
  • Received:2005-01-08 Revised:2006-01-06 Online:2006-08-25 Published:2006-08-25
  • Contact: Chu Yuming

Abstract: et DoverlineR2 be a simply connected domain with boundary containing
at least three points, and for any x, y∈ D, aD(x, y) denote theApollonian metric in D with respect to x and y. A. F. Beardon gave the following conjecture in 1998: If f: D →D be an Apollonian isometry,then f is a M"obius transformation.In this paper, the author affirms and proves the conjecture when D is a disk.

Key words: Apollonian metric, Isometry, Mobius tranformation, Disk

CLC Number: 

  • 30C65
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