New York Journal of Mathematics
Volume 23 (2017) 315-349


Jason DeBlois

Bounding the area of a centered dual two-cell below, given lower bounds on its side lengths

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

For a locally finite set S in the hyperbolic plane, suppose C is a compact, n-edged two-cell 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 n-tuple of positive real numbers bounding its side lengths below, and for n≦ 9 implement an algorithm to compute this bound. For geometrically reasonable side-length bounds, we expect the area bound to be sharp or near-sharp.

Author information

Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260