An improved bound on the Minkowsik dimension of Besicovitch sets in R^3

• Autores: Izabella Laba, Terence Tao, Nets Hawk Katz
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 152, Nº 2, 2000, págs. 383-446
• Idioma: inglés
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• Resumen

  • A Besicovitch set is a set which contains a unit line segment in any direction. It is known that the Minkowski and Hausdorff dimensions of such a set must be greater than or equal to 5/2 in R3. In this paper we show that the Minkowski dimension must in fact be greater than 5/2 + " for some absolute constant " > 0. One observation arising from the argument is that Besicovitch sets of near-minimal dimension have to satisfy certain strong properties, which we call ¿stickiness,¿ ¿planiness,¿ and ¿graininess.¿