Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes
We present a constructive proof of Alexandrov's theorem on the existence of a convex
polytope with a given metric on the boundary. The polytope is obtained by deforming certain …
polytope with a given metric on the boundary. The polytope is obtained by deforming certain …
Discrete conformal variations and scalar curvature on piecewise flat two-and three-dimensional manifolds
D Glickenstein - Journal of Differential Geometry, 2011 - projecteuclid.org
A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge
lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider …
lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider …
Decorated discrete conformal maps and convex polyhedral cusps
We discuss a notion of discrete conformal equivalence for decorated piecewise Euclidean
surfaces (PE-surface), that is, PE-surfaces with a choice of circle about each vertex. It is …
surfaces (PE-surface), that is, PE-surfaces with a choice of circle about each vertex. It is …
The unified discrete surface Ricci flow
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the
curvature evolves according to a heat diffusion process and eventually becomes constant …
curvature evolves according to a heat diffusion process and eventually becomes constant …
Decorated discrete conformal equivalence in non-Euclidean geometries
We introduce decorated piecewise hyperbolic and spherical surfaces and discuss their
discrete conformal equivalence. A decoration is a choice of circle about each vertex of the …
discrete conformal equivalence. A decoration is a choice of circle about each vertex of the …
Survey on discrete surface Ricci flow
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the
curvature evolves according to a nonlinear heat diffusion process, and becomes constant …
curvature evolves according to a nonlinear heat diffusion process, and becomes constant …
Local rigidity of inversive distance circle packing
R Guo - Transactions of the American Mathematical Society, 2011 - ams.org
LOCAL RIGIDITY OF INVERSIVE DISTANCE CIRCLE PACKING 1. Introduction 1.1.
Andreev-Thurston Theorem. In his work on constructing h Page 1 TRANSACTIONS OF THE …
Andreev-Thurston Theorem. In his work on constructing h Page 1 TRANSACTIONS OF THE …
Faddeev–Volkov solution of the Yang–Baxter equation and discrete conformal symmetry
The Faddeev–Volkov solution of the star-triangle relation is connected with the modular
double of the quantum group Uq (sl2). It defines an Ising-type lattice model with positive …
double of the quantum group Uq (sl2). It defines an Ising-type lattice model with positive …
Ideal hyperbolic polyhedra and discrete uniformization
B Springborn - Discrete & Computational Geometry, 2020 - Springer
We provide a constructive, variational proof of Rivin's realization theorem for ideal
hyperbolic polyhedra with prescribed intrinsic metric, which is equivalent to a discrete …
hyperbolic polyhedra with prescribed intrinsic metric, which is equivalent to a discrete …
[HTML][HTML] Rigidity of inversive distance circle packings revisited
X Xu - Advances in Mathematics, 2018 - Elsevier
Inversive distance circle packing metric was introduced by P Bowers and K Stephenson [7]
as a generalization of Thurston's circle packing metric [34]. They conjectured that the …
as a generalization of Thurston's circle packing metric [34]. They conjectured that the …