A Besicovitch set in AG(n,q) is a set of points containing a line in every
direction. The Kakeya problem is to determine the minimal size of such a set.
We solve the Kakeya problem in the plane, and substantially improve the known
bounds for n greater than 4.Comment: 13 page

A. Bichara

A. Blokhuis

A. E. Brouwer

B. Segre

P. J. Cameron

R. Jamison

T. Tao

T. Wolff

X. W. C. Faber

English

arXiv

Crossref

The Finite Field Kakeya Problem

A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4

Blokhuis, A.

Mazzocca, F.

NARCIS 

The finite field Kakeya problem

Blokhuis, A Aart

Mazzocca, F

Repository TU/e

Let AG(n,q) the n-dimensional affine space over a finite field with q elements. A Kakeya set is a point set of AG(n,q) which contains a line in every direction. Is it true that every Kakeya set must have cardinality at least  , where   is a constant depending only on the dimension  , but not on q? This question (the finite field Kakeya problem) was first formulated in an expository paper by Tom Wolff in the late 1990s, and addressed in several subsequent papers (Mockenhaupt-Tao 2004, Tao 2005, Bourgain-Katz-Tao 2004). In this paper the problem is completely solved in the case n=2; more precisely, Kakeya sets of minimal size in AG(2,q) are characterized. Some application of this result to blocking sets is showe

BLOKHUIS A.

MAZZOCCA, Francesco

Archivio Istituzionale della Ricerca - Università degli Studi della Campania "Luigi Vanvitelli"

Pure OAI Repository

A Besicovitch set in AG(n; q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n &gt; 4

A Besicovitch set in AG(n, q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n&gt; 4. 

Aart Blokhuis

Francesco Mazzocca

CiteSeerX

The Finite Field Kakeya Problem

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NARCIS

Repository TU/e

Archivio Istituzionale della Ricerca - Università degli Studi della Campania "Luigi Vanvitelli"

Pure OAI Repository

Repository TU/e

CiteSeerX

Pure OAI Repository

Pure OAI Repository