Search
Search Results
-
The character of Thurston’s circle packings
We introduce the character of Thurston’s circle packings in the hyperbolic background geometry Consequently, some quite simple criteria are obtained...
-
Circle packings from tilings of the plane
We introduce a new class of fractal circle packings in the plane, generalizing the polyhedral packings defined by Kontorovich and Nakamura. The...
-
On the Deformation of Thurston’s Circle Packings with Obtuse Intersection Angles
We study Thurston’s circle packings with obtuse intersection angles on closed surfaces. By using combinatorial Ricci/Calabi flows and variational...
-
A Geometric Study of Circle Packings and Ideal Class Groups
A family of fractal arrangements of circles is introduced for each imaginary quadratic field K . Collectively, these arrangements contain (up to an...
-
Ball Packings in Hyperbolic Space
It is natural to extend the study of packing and covering problems to the hyperbolic plane, as well as hyperbolic spaces of higher dimension....
-
Rigidity and deformation of generalized sphere packings on 3-dimensional manifolds with boundary
Motivated by Guo–Luo’s generalized circle packings on surfaces with boundary (Guo–Luo in Geom Topol 13(3):1265–1312, 2009), we introduce the...
-
Thurston’s sphere packings on 3-dimensional manifolds, I
Thurston’s sphere packing on a 3-dimensional manifold is an analogue of Thurston’s circle packing on a surface, the rigidity of which has been open...
-
Density of Binary Disc Packings: The Nine Compact Packings
A disc packing in the plane is compact if its contact graph is a triangulation. There are nine values of r such that a compact packing by discs of...
-
-
Voronoi tiling and circle packing on spiral lattices with rotational symmetry
It is shown that the bifurcation diagram of circle packings on logarithmic spiral lattices with rotational symmetry is graph-theoretically dual to...
-
Apollonian packings in seven and eight dimensions
In an earlier work, we proposed a generalization for the Apollonian packing in arbitrary dimensions and showed that the resulting object in four,...
-
-
-
Recurrence of a weighted random walk on a circle packing with parabolic carrier
In this paper we show that given a circle packing of an infinite planar triangulation such that its carrier is parabolic, placing weights on the...
-
Deformation of discrete conformal structures on surfaces
In Glickenstein (J Differ Geom 87: 201–237, 2011), Glickenstein introduced the discrete conformal structures on polyhedral surfaces in an axiomatic...
-
Efficiency of Packings and Coverings with a Sequence of Convex Disks
We search for those convex disks which are: 1) the least efficient for packing the plane, 2) the least efficient for covering it. Thus, in a certain...
-
Improved interval methods for solving circle packing problems in the unit square
In this work computer-assisted optimality proofs are given for the problems of finding the densest packings of 31, 32, and 33 non-overlap** equal...
-
Homothetic packings of centrally symmetric convex bodies
A centrally symmetric convex body is a convex compact set with non-empty interior that is symmetric about the origin. Of particular interest are...
-
Numerical Methods for Constructing Suboptimal Packings of Nonconvex Domains with Curved Boundary
AbstractWe study the problem of constructing some optimal packings of simply-connected nonconvex plane domains with a union of congruent circles. We...
