Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An improved bound on the Minkowski dimension of Besicovitch sets in R^3   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 \R^3. In this paper we show that
the Minkowski dimension must in fact be greater than 5/2 + \epsilon for some
absolute constant \epsilon > 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.''
  The purpose of this paper is to improve upon the known bounds for the
Minkowski dimension of Besicovitch sets in three dimensions. As a by-product of
the argument we obtain some strong conclusions on the structure of Besicovitch
sets with almost-minimal Minkowski dimension.

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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg