Add to ORKGWe discuss recent work of several authors on the Kakeya needle problem and other related problems involving nonexistence of small sets containing large families of one dimensional objects
A Besicovitch set is a subset of R d that contains a unit line segment in every direction and the fa...
We study the almost everywhere behavior of the maximal operator associated to moving averages in the...
We answer an old question: what are possible growth rates of the expected number of vector-maximal p...
A Kakeya, or Besicovitch, set in a vector space is a set which contains a line in every direction. T...
We address the two-dimensional Knapsack Problem (2KP), aimed at packing a maximum-prot subset of rec...
A maximal vector of a set is one which is not less than any other vector in all components. We deriv...
This document is composed of a series of articles in discrete geometry, each solving a problem in pa...
We study the analogues of the problems of averages and maximal averages over a surface in Rn when th...
Abstract. We study the analogues of the problems of averages and maximal averages over a surface in ...
A Besicovitch set in AG(n; q) is a set of points containing a line in every direction. The Kakeya pr...
In this work we de fine Hausdorff measure and dimension, describe the geometrical construction of a ...
The Kakeya maximal function conjecture is a quantitative, single scale formulation of the Kakeya con...
AbstractLet m be an integer ⩾ 2. The effect of crowding m unit vectors x1,…,xm into the real Euclide...
A Kakeya set is a subset of Rd that contains a unit line segment in every direction. Let S̊d−1 denot...
We propose and study the following problem: given $X \subset Z_n$, construct a maximum packing of $d...
A Besicovitch set is a subset of R d that contains a unit line segment in every direction and the fa...
We study the almost everywhere behavior of the maximal operator associated to moving averages in the...
We answer an old question: what are possible growth rates of the expected number of vector-maximal p...
A Kakeya, or Besicovitch, set in a vector space is a set which contains a line in every direction. T...
We address the two-dimensional Knapsack Problem (2KP), aimed at packing a maximum-prot subset of rec...
A maximal vector of a set is one which is not less than any other vector in all components. We deriv...
This document is composed of a series of articles in discrete geometry, each solving a problem in pa...
We study the analogues of the problems of averages and maximal averages over a surface in Rn when th...
Abstract. We study the analogues of the problems of averages and maximal averages over a surface in ...
A Besicovitch set in AG(n; q) is a set of points containing a line in every direction. The Kakeya pr...
In this work we de fine Hausdorff measure and dimension, describe the geometrical construction of a ...
The Kakeya maximal function conjecture is a quantitative, single scale formulation of the Kakeya con...
AbstractLet m be an integer ⩾ 2. The effect of crowding m unit vectors x1,…,xm into the real Euclide...
A Kakeya set is a subset of Rd that contains a unit line segment in every direction. Let S̊d−1 denot...
We propose and study the following problem: given $X \subset Z_n$, construct a maximum packing of $d...
A Besicovitch set is a subset of R d that contains a unit line segment in every direction and the fa...
We study the almost everywhere behavior of the maximal operator associated to moving averages in the...
We answer an old question: what are possible growth rates of the expected number of vector-maximal p...