Vol. 258, No. 1, 2012

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Delaunay cells for arrangements of flats in hyperbolic space

Andrew Przeworski

Vol. 258 (2012), No. 1, 223–256
Abstract

For n + 1 disjoint flats of dimension k in n, we produce a Delaunay cell that is a generalization of the Delaunay simplex associated to n + 1 points in n. Combinatorially, these Delaunay cells resemble truncated n-dimensional simplices. For certain classes of arrangements of flats in n, we prove that these Delaunay cells can be glued together to form a Delaunay complex, with the result that almost every point of n 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
Authors
Andrew Przeworski
Department of Mathematics
College of Charleston
66 George St.
Charleston, SC 29424
http://przeworskia.people.cofc.edu