Separated sets and the Falconer conjecture for polygonal norms

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dc.creatorKonyagin, Sergei
dc.creatorLaba, Izabella
dc.date2004-07-28
dc.date.accessioned2026-07-07T05:10:48Z
dc.date.available2026-07-07T05:10:48Z
dc.descriptionThe Falconer conjecture asserts that if E is a planar set with Hausdorff dimension strictly greater than 1, then its Euclidean distance set has positive one-dimensional Lebesgue measure. We discuss the analogous question with the Euclidean distance replaced by non-Euclidean norms in which the unit ball is a polygon with 2K sides. We prove that for any such norm there is a set of Hausdorff dimension K/(K-1) whose distance set has Lebesgue measure 0.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0407503
dc.identifierhttp://arxiv.org/abs/math/0407503
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72047
dc.subjectMetric Geometry
dc.subject28A78
dc.titleSeparated sets and the Falconer conjecture for polygonal norms
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