35
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Quasiregular mapping by branched circle packing

&
Pages 667-673 | Received 08 Sep 2006, Accepted 12 Dec 2007, Published online: 22 Sep 2010

References

  • Begehr , H . 1994 . Complex Analytic Methods for Partial Differential Equations: An Introductory Text , Singapore : World Scientific .
  • Rickman , S . 1993 . Quasiregular Mappings , Berlin Heidelberg : Springer-Verlag .
  • Thurston , W . 1985 . The Finite Riemann Mapping Theorem, invited address, International Symposium in Celebration of the Proof of the Bieberbach Conjecture , West Lafayette, , USA : Purdue University .
  • Rodin , B and Sullivan , D . 1987 . The convergence of circle packings to the Riemann mapping . J. Differ. Geom , 26 : 349 โ€“ 360 .
  • Stephenson , K . 2005 . Introduction to Circle Packing: The Theory of Discrete Analytic Functions , New York, , USA : Cambridge University Press .
  • He , ZX . 1990 . Solving Beltrami equations by circle packing . Trans. Amer. Math. Soc , 322 : 657 โ€“ 670 .
  • Williams , GB . 2006 . A circle packing measurable Riemann mapping theorem . Proc. Amer. Math. Soc , 134 : 2139 โ€“ 2146 .
  • Lan , SY and Dai , DQ . 2004 . On Riemann mapping theorems for Beltrami equations by circle packings . Pacific, J. Math , 217 : 139 โ€“ 148 .
  • Bonk , M and Heinonen , J . 2004 . Smooth quasiregular mappings with branching . Publ. Math. Inst. Hauter Edes Sci , 100 : 153 โ€“ 170 .
  • Rudin , W . 1980 . Function Theory in the Unit Ball of โ„‚ n , New York : Springer-Verlag .
  • Dubejko , T . 1995 . Branched circle packings and discrete Blaschke products . Trans. Amer. Math. Soc , 347 : 4073 โ€“ 4103 .
  • Lehto , O and Virtanen , KI . 1973 . Quasiconformal Mapping in the Plane , 2nd , New York : Springer-Verlag .
  • Dubejko , T . 1997 . Infinite branched circle packings and discrete complex polynomials . J. London Math. Soc , 56 : 347 โ€“ 368 .
  • Cater , I and Rodin , B . 1992 . An inverse problem for circle packing and conformal mappings . Trans. Amer. Math. Soc , 334 : 861 โ€“ 875 .
  • Ya Gutlyanskii , V . 2000 . Infinitesimal geometry of quasiregular mappings . Ann. Acad. Sci. Fenn. Math , 25 : 101 โ€“ 130 .
  • Matthes , D . 2005 . Convergence in discrete Cauchy problems and applications to circle patterns . Conf. Geom. Dyn , 9 : 1 โ€“ 23 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.