Hyperbolic geometry and the Hillam-Thron theorem
نویسنده
چکیده
Every open ball within R∞ has an associated hyperbolic metric and Möbius transformations act as hyperbolic isometries from one ball to another. The Hillam-Thron Theorem is concerned with images of balls under Möbius transformation, yet existing proofs of the theorem do not make use of hyperbolic geometry. We exploit hyperbolic geometry in proving a generalisation of the Hillam-Thron Theorem and examine the precise configurations of points and balls that arise in that theorem.
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