WebbSets or Kakeya Sets. The Kakeya conjectures states that the Hausdorff dimension of any Besicovitch Sets in Rn is n. The case for n≥ 3 is still an open problem. The so-called … Webb10 dec. 2009 · THE KAKEYA SET AND MAXIMAL CONJECTURES FOR ALGEBRAIC VARIETIES OVER FINITE FIELDS Part of: Finite geometry and special incidence …
Polynomial Wolff axioms and Kakeya-type estimates in
Webb10 mars 2009 · The Kakeya set and maximal conjectures for algebraic varieties over finite fields Jordan Ellenberg, Richard Oberlin, Terence Tao Using the polynomial method of … WebbSets or Kakeya Sets. The Kakeya conjectures states that the Hausdorff dimension of any Besicovitch Sets in Rn is n. The case for n≥ 3 is still an open problem. The so-called maximal Kakeya conjecture (or maximal Nikodym conjecture) is actually a stronger one that involves the following Kakeya maximal function (or Nikodym maximal function): f∗ difference between high gloss and satin
Kakeya set Detailed Pedia
Webb16 feb. 2001 · The Kakeya conjecture on local fields of positive characteristic Alejo Salvatore Mathematics Mathematika 2024 We state and prove an analogue of the Kakeya conjecture for the local field Fq ( (t))$\mathbb {F}_q (\! (t)\!)$ . This extends Arsovski's result on the Kakeya conjecture to local fields of positive… 1 PDF Kakeya maximal function conjecture: For all ε > 0, there exists a constant Cε > 0 such that for any function f and all δ > 0, (see lp space for notation) Results [ edit] Some results toward proving the Kakeya conjecture are the following: The Kakeya conjecture is true for n = 1 (trivially) and n = 2 (Davies [8] ). Visa mer In mathematics, a Kakeya set, or Besicovitch set, is a set of points in Euclidean space which contains a unit line segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane, or a ball of radius 1/2 … Visa mer The Kakeya needle problem asks whether there is a minimum area of a region $${\displaystyle D}$$ in the plane, in which a needle of unit … Visa mer Statement The same question of how small these Besicovitch sets could be was then posed in higher dimensions, giving rise to a number of conjectures known collectively as the Kakeya conjectures, and have helped initiate the … Visa mer Sets containing circles and spheres Analogues of the Kakeya problem include considering sets containing more general shapes than lines, … Visa mer Besicovitch was able to show that there is no lower bound > 0 for the area of such a region $${\displaystyle D}$$, in which a needle of unit length can be turned around. That is, for every $${\displaystyle \varepsilon >0}$$, there is region of area One method of … Visa mer Somewhat surprisingly, these conjectures have been shown to be connected to a number of questions in other fields, notably in harmonic analysis. For instance, in 1971, Visa mer • Nikodym set Visa mer Webb10 mars 2009 · The Kakeya set and maximal conjectures for algebraic varieties over finite fields Jordan Ellenberg, Richard Oberlin, Terence Tao Using the polynomial method of Dvir \cite {dvir}, we establish optimal estimates for Kakeya sets and Kakeya maximal functions associated to algebraic varieties over finite fields . forklift accident on aurora