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dc.contributor.authorGonzález Merino, Bernardo
dc.contributor.authorHenze, Matthias
dc.date.accessioned2016-05-10T12:00:04Z
dc.date.accessioned2016-10-05T14:14:06Z
dc.date.available2016-05-10T12:00:04Z
dc.date.available2016-10-05T14:14:06Z
dc.date.issued2016-05-10
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1118
dc.descriptionResearch in Pairs 2014en_US
dc.description.abstractIn 1978, Makai Jr. established a remarkable connection between the volume-product of a convex body, its maximal lattice packing density and the minimal density of a lattice arrangement of its polar body intersecting every affine hyperplane. Consequently, he formulated a conjecture that can be seen as a dual analog of Minkowski’s fundamental theorem, and which is strongly linked to the well-known Mahlerconjecture. Based on the covering minima of Kannan & Lovász and a problem posed by Fejes Tóth, we arrange Makai Jr.’s conjecture into a wider context and investigate densities of lattice arrangements of convex bodies intersecting every i-dimensional affine subspace. Then it becomes natural also to formulate and study a dual analog to Minkowski’s second fundamental theorem. As our main results, we derive meaningful asymptotic lower bounds for the densities of such arrangements, and furthermore, we solve the problems exactly for the special, yet important, class of unconditional convex bodies.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2016,08
dc.titleOn densities of lattice arrangements intersecting every i-dimensional affine subspaceen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2016-08
local.scientificprogramResearch in Pairs 2014
local.series.idOWP-2016-08
dc.identifier.urnurn:nbn:de:101:1-201605115634
dc.identifier.ppn1656555433


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