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Original Articles

Conformally Symmetric Circle Packings: A Generalization of Doyle's Spirals

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Pages 141-150 | Published online: 04 Apr 2012

REFERENCES

  • Agafonov , S. I. and Bobenko , A. I. 2000 . “Discrete zϒ and Painlevéequations” . Internal. Math. Res. Notices , 2000 ( 4 ) : 165 – 193 . [Agafonov and Bobenko 2000]
  • Beardon , A. F. and Stephenson , K. 1990 . “The uniformization theorem for circle packings” . Indiana Univ. Math. J. , 39 ( 4 ) : 1383 – 1425 . [Beardon and Stephenson 1990]
  • Beardon , A. F. , Dubejko , T. and Stephenson , K. 1994 . “Spiral hexagonal circle packings in the plane” . Geom. Dedicata , 49 ( 1 ) : 39 – 70 . [Beardon et al. 1994]
  • Bobenko , A. I. and Pinkall , U. 1999 . “Discretization of surfaces and integrable systems”. ” . In Discrete integrable geometry and physics Edited by: Bobenko , A. I. and Seiler , R. 3 – 58 . Oxford : Oxford Univ. Press. . [Bobenko and Pinkall 1999], Oxford Lecture Ser. Math. Appl. 16
  • Callahan , K. and Rodin , B. 1993 . “Circle packing immersions form regularly exhaustible surfaces” . Complex Variables Theory Appl. , 21 ( 3–4 ) : 171 – 177 . [Callahan and Rodin 1993]
  • Dubejko , T. and Stephenson , K. 1995 . “Circle packing: experiments in discrete analytic function theory” . Experiment. Math. , 4 ( 4 ) : 307 – 348 . [Dubejko and Stephenson 1995]
  • He , Z.-X. and Schramm , O. 1998 . “The C∝-convergence of hexagonal disk packings to the Riemann map” . Acta Math. , 180 ( 2 ) : 219 – 245 . [He and Schramm 1998]
  • Rodin , B. 1987 . “Schwarz's lemma for circle packings” . Invent. Math. , 89 ( 2 ) : 271 – 289 . [Rodin 1987]
  • Rodin , B. and Sullivan , D. 1987 . “The convergence of circle packings to the Riemann mapping” . J. Differential Geom. , 26 ( 2 ) : 349 – 360 . [Rodin and Sullivan 1987]
  • Schramm , O. 1997 . “Circle patterns with the combinatorics of the square grid” . Duke Math. J. , 86 ( 2 ) : 347 – 389 . [Schramm 1997]
  • Schramm , O. 1998 . “Circle packings and con-formal geometry, a survey of selected topics” [Schramm 1998], See http://www.math.weizmann.ac.il/-schramm/talks
  • Spanier , J. and Oldham , K. B. 1987 . An atlas of functions Washington : Hemisphere Pub. Corp. . [Spanier and Oldham 1987]
  • Thurston , W. P. 1985 . “The finite Riemann mapping theorem” [Thurston 1985], Invited address, International Symposium in Celebration of the Proof of the Bieberbach Conjecture, Purdue University

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