 

Jason DeBlois
Bounding the area of a centered dual twocell below, given lower bounds on its side lengths view print


Published: 
March 8, 2017 
Keywords: 
hyperbolic surface, Delaunay triangulation, effective algorithm 
Subject: 
57M50, 52C15 


Abstract
For a locally finite set S in the hyperbolic plane, suppose C is a compact, nedged twocell of the centered dual complex of S, a coarsening of the Delaunay tessellation introduced in the author's prior work. We describe an effectively computable lower bound for the area of C, given an ntuple of positive real numbers bounding its side lengths below, and for n≦ 9 implement an algorithm to compute this bound. For geometrically reasonable sidelength bounds, we expect the area bound to be sharp or nearsharp.


Author information
Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260
jdeblois@pitt.edu

