Acta mathematica scientia,Series A
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Chu Yuming
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Abstract: et DoverlineR2 be a simply connected domain with boundary containingat 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
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Chu Yuming. Apollonian Isometries and Mobius Transformations[J].Acta mathematica scientia,Series A, 2006, 26(4): 522-526.
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