Introduction to Circle Packing: The Theory of Discrete Analytic Functions

By Kenneth Stephenson. 2005

360 citations recorded by the source corpus.

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Citations in the corpus

A variational principle for weighted Delaunay triangulations and hyperideal polyhedra (2006, background): “of curvature connect one marked ideal vertex with the other hyperideal vertices. 1.3. Related work. For acomprehensivebibliographyoncirclepackingsandcircle patterns we refer to Stephenson’s monograph [34]. Here, we can only attempt to brieﬂy discuss some of the the most important and most closely re”
A discrete uniformization theorem for polyhedral surfaces II (2014, background): “See [22] for the corresponding discrete conformal maps for circle packing.”
Numerical Computation of Surface Conformal Mappings (2012, methodology): “Circle packing methods lead to the theory of discrete analytic function [60], which is one of the few planar methods that has actually been used for surface maps.”
Rigidity of inversive distance circle packings revisited (2017, methodology): “Bowers and Stephenson [7] once conjectured that the inversive distance circle packings are rigid.”
Geometric representations of graphs (2014, background): “There is a book on this subject by Kenneth Stephenson [190].”
Discrete conformal maps and ideal hyperbolic polyhedra (2010, background): “h was later proved by Rodin and Sullivan [31], set off a ﬂurry of research that lead to a fullﬂedged theory of discrete analytic functions and conformal maps based on packings and patterns of circles [35]. (The circle packing version of Luo’s discrete Yamabe ﬂow is the discrete Ricci ﬂow of Chow and”
Local rigidity of inversive distance circle packing (2009, background): “P. L. Bowers, K. Stephenson, Uniformizing dessins and Bely̆ı maps via circle packing.”
Discrete conformal variations and scalar curvature on piecewise flat two and three dimensional manifolds (2009, background): “Remark 30 Special cases of this theorem appear in [23][17][18][19] and less refined versions (where only signs and not explicit values are computed for the derivatives) appear in many other places, including [44][39][29][43].”
Rectangle and Square Representations of Planar Graphs (2013, background): “From there the theory has developed into a discrete analog of complex analysis, Stephenson’s book [Ste05] gives a comprehensive introduction.”
A discrete uniformization theorem for polyhedral surfaces (2013, background): “See [22] for the corresponding discrete conformal maps for circle packing.”
On the deformation of inversive distance circle packings, III (2016, background): “als to the following convex set n x∈ RN XN i=1 xi = 2πχ(M) o\ \ φ6= A$V YΦ A . (5.2) For a proof, see Thurston [21], Marden-Rodin [18], Colin de Verdi`ere [7], He [12], Chow-Luo [6] and Stephenson [20]. Note that the existence of constant curvature metric is equivalent to Kav1 ∈ K(RN >0). Substi”