Characterizing the Delaunay decompositions of compact hyperbolic surfaces
نویسنده
چکیده
Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the “empty disks” circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decomposition and angle assignment can be realized as the data of an actual Delaunay decomposition of a hyperbolic surface. AMS Classification numbers Primary: 52C26 Secondary: 30F10
منابع مشابه
Research Summary
In my doctoral dissertation (directed by W. P. Thurston) I studied the geometry of convex polyhedra in hyperbolic 3-space H3, and succeeded in producing a geometric characterization of dihedral angles of compact convex polyhedra by reducing the question to a convex isometric embedding problem in the De Sitter sphere, and resolving this problem. In particular, this produced a simple alternative ...
متن کاملDelaunay Triangulations on Orientable Surfaces of Low Genus
Earlier work on Delaunay triangulation of point sets on the 2D flat torus, which is locally isometric to the Euclidean plane, was based on lifting the point set to a locally isometric 9-sheeted covering space of the torus [28, 20, 12, 11]. Under mild conditions the Delaunay triangulation of the lifted point set, consisting of 9 copies of the input set, projects to the Delaunay triangulation of ...
متن کاملExplicit Parametrization of Delaunay Surfaces in Space Forms via Loop Group Methods
We compute explicit conformal parametrizations of Delaunay surfaces in each of the three space forms Euclidean 3-space , spherical 3-space 3 and hyperbolic 3-space 3 by using the generalized Weierstrass type representation for constant mean curvature (CMC) surfaces established by J. Dorfmeister, F. Pedit and H. Wu.
متن کاملA Natural Parameterization of the Roulettes of the Conics Generating the Delaunay Surfaces
Communicated by John Oprea Abstract. We derive parametrizations of the Delaunay constant mean curvature surfaces of revolution that follow directly from parametrizations of the conics that generate these surfaces via the corresponding roulette. This uniform treatment exploits the natural geometry of the conic (parabolic, elliptic or hyperbolic) and leads to simple expressions for the mean and G...
متن کاملCharacterizing Delaunay Graphs via Fixed Point Theorem
This paper discusses a problem for determining whether a given plane graph is a Delaunay graph, i.e., whether it is topologically equivalent to a Delaunay triangulation. There exists a theorem which characterizes Delaunay graphs and yields a polynomial time algorithm for the problem only by solving a certain linear inequality system. The theorem was proved by Rivin based on arguments of hyperbo...
متن کامل