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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Squaring rectangles for dumbbells


Authors: J. W. Cannon, W. J. Floyd and W. R. Parry
Journal: Conform. Geom. Dyn. 12 (2008), 109-132
MSC (2000): Primary 52C20, 52C26
Published electronically: August 14, 2008
MathSciNet review: 2434355
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Abstract: The theorem on squaring a rectangle (see Schramm [Israel J. Math. 84 (1993)] and Cannon-Floyd-Parry [Contemp. Math. 169, AMS, 1994]) gives a combinatorial version of the Riemann mapping theorem. We elucidate by example (the dumbbell) some of the limitations of rectangle-squaring as an approximation to the classical Riemann mapping.


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Additional Information

J. W. Cannon
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: cannon@math.byu.edu

W. J. Floyd
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
Email: floyd@math.vt.edu

W. R. Parry
Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
Email: walter.parry@emich.edu

DOI: http://dx.doi.org/10.1090/S1088-4173-08-00182-3
PII: S 1088-4173(08)00182-3
Keywords: Finite subdivision rules, combinatorial moduli, squaring rectangles
Received by editor(s): June 19, 2008
Published electronically: August 14, 2008
Article copyright: © Copyright 2008 American Mathematical Society