Local rigidity of inversive distance circle packing
By Ren Guo. 2009
84 citations recorded by the source corpus.
A Euclidean (or hyperbolic) circle packing on a closed triangulated surface with prescribed inversive distance is locally determined by its cone angles. We prove this by applying a variational principle.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/82e471ceb2d7573847d122b1f26595537fd8bce1
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Rigidity of Polyhedral Surfaces, III (2010, unknown): “G T ]”
- Rigidity of polyhedral surfaces, II (2006, methodology): “Guo also proved [9] that the open sets where the 1–forms w are defined in Theorem 3.”
- On the deformation of inversive distance circle packings, III (2016, methodology): “tices that face the edge {23}, {13} and {12} respectively. Moreover, let θi be the inner angle at vertex ifor each i∈ {1,2,3}. Thus we get the angle map θ= (θ1,θ2,θ3)T : ∆ → R3 >0. Lemma 3.1. (Guo [11]) For each (r1,r2,r3)T ∈ ∆, let ui = lnri for each i∈ {1,2,3}. The Jacobian matrix ∂(θ1,θ2,θ3) ∂”
- Rigidity of inversive distance circle packings revisited (2017, methodology): “We refer to Glickenstein [18] for a nice geometric interpretation of the variational principle in [19].”
- Numerical Computation of Surface Conformal Mappings (2012, background): “The edge length are given by (17) l ij = cosh − 1 ( cosh g i cosh g j + sinh g i sinh g j I ij ) in hyperbolic geometry, e.g. [33] and [70].”