
Flipping Geometric Triangulations on Hyperbolic Surfaces
We consider geometric triangulations of surfaces, i.e., triangulations w...
read it

Delaunay triangulations of generalized Bolza surfaces
The Bolza surface can be seen as the quotient of the hyperbolic plane, r...
read it

Predicting Future Cognitive Decline with Hyperbolic Stochastic Coding
Hyperbolic geometry has been successfully applied in modeling brain cort...
read it

Feedback game on 3chromatic Eulerian triangulations of surfaces
In this paper, we study the feedback game on 3chromatic Eulerian triang...
read it

Eccentricity terrain of δhyperbolic graphs
A graph G=(V,E) is δhyperbolic if for any four vertices u,v,w,x, the tw...
read it

Parametric polynomial minimal surfaces of arbitrary degree
Weierstrass representation is a classical parameterization of minimal su...
read it

Annihilation Operators for Exponential Spaces in Subdivision
We investigate properties of differential and difference operators annih...
read it
Minimal Delaunay triangulations of hyperbolic surfaces
Motivated by recent work on Delaunay triangulations of hyperbolic surfaces, we consider the minimal number of vertices of such triangulations. First, we will show that every hyperbolic surface of genus g has a simplicial Delaunay triangulation with O(g) vertices, where edges are given by distance paths. Then, we will construct a class of hyperbolic surfaces for which the order of this bound is optimal. Finally, to give a general lower bound, we will show that the Ω(√(g)) lower bound for the number of vertices of a simplicial triangulation of a topological surface of genus g is tight for hyperbolic surfaces as well.
READ FULL TEXT
Comments
There are no comments yet.