Delaunay cells for arrangements of flats in hyperbolic space

Andrew Przeworski

Vol. 258 (2012), No. 1, 223–256

DOI: 10.2140/pjm.2012.258.223

Abstract

For n + 1 disjoint flats of dimension k in ℍⁿ, we produce a Delaunay cell that is a generalization of the Delaunay simplex associated to n + 1 points in ℍⁿ. Combinatorially, these Delaunay cells resemble truncated n-dimensional simplices. For certain classes of arrangements of flats in ℍⁿ, we prove that these Delaunay cells can be glued together to form a Delaunay complex, with the result that almost every point of ℍⁿ is in a total of one Delaunay cell, counting with multiplicities and orientations.

Keywords

Delaunay, hyperbolic, flats

Mathematical Subject Classification 2010

Primary: 51M09, 52C17, 57M50

Milestones

Received: 10 August 2011

Accepted: 30 May 2012

Published: 21 July 2012