Limits of Voronoi Diagrams

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dc.creatorLindenbergh, Roderik
dc.date2002-10-22
dc.date.accessioned2026-07-07T04:52:14Z
dc.date.available2026-07-07T04:52:14Z
dc.descriptionIn this thesis we study sets of points in the plane and their Voronoi diagrams, in particular when the points coincide. We bring together two ways of studying point sets that have received a lot of attention in recent years: Voronoi diagrams and compactifications of configuration spaces. We study moving and colliding points and this enables us to introduce `limit Voronoi diagrams'. We define several compactifications by considering geometric properties of pairs and triples of points. In this way we are able to define a smooth, real version of the Fulton-MacPherson compactification. We show how to define Voronoi diagrams on elements of these compactifications and describe the connection with the limit Voronoi diagrams.
dc.descriptionPhD thesis, 132 pages, lots of figures
dc.identifierhttps://arxiv.org/abs/math/0210345
dc.identifierhttp://arxiv.org/abs/math/0210345
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65393
dc.subjectMetric Geometry
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subjectGeometric Topology
dc.subject05A15, 06A07, 32S45, 51K99, 51M20, 52C35, 57N80, 68U05
dc.titleLimits of Voronoi Diagrams
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