Conformal Geometry and Dynamics

Author(s): J. W. Cannon; W. J. Floyd; W. R. Parry
Journal: Conform. Geom. Dyn. 12 (2008), 109-132.
MSC (2000): Primary 52C20, 52C26
Posted: August 14, 2008
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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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2.: J. W. Cannon, W. J. Floyd, and W. R. Parry, Finite subdivision rules, Conform. Geom. Dyn. 5 (2001), 153-196 (electronic). MR 1875951 (2002j:52021)
3.: J. W. Cannon, W. J. Floyd, and W. R. Parry, Expansion complexes for finite subdivision rules I, Conform. Geom. Dyn. 10 (2006), 63-99 (electronic). MR 2218641 (2007c:30048)
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7.: K. Stephenson, CirclePack, software, available from http://www.math.utk.edu/˜kens.

Retrieve articles in Conformal Geometry and Dynamics with MSC (2000): 52C20, 52C26

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: 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
Posted: August 14, 2008
Copyright of article: Copyright 2008, American Mathematical Society

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