WebFeb 16, 2001 · New bounds on Kakeya problems. Nets Katz, Terence Tao. We establish new estimates on the Minkowski and Hausdorff dimensions of Besicovitch sets and obtain … Webinformation about this mysterious Hausdor dimension that turns so di cult to establish for Kakeya sets. More popular surveys about such connections are the one by Wol [19] and the one by Tao [14]. In this paper, we will focus only on one particular analogue which Wol proposed in 1999 in [18]: the nite eld version of the Kakeya problem.
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WebSep 17, 2003 · Besides being an interesting problem in incidence geometry, it also caught the attention of harmonic analysts due to connections to the Kakeya problem as observed by Wolff [Wol99]. This connection ... WebSep 24, 2008 · The Kakeya Problem for Simply Connected and for Star-shaped Sets. by Frederick Cunningham, Jr. Year of Award: 1972. Publication Information: The American …
WebAnalogues and Generalizations of the Kakeya problem 1. The solution of Kakeya’s problem for convex sets is an equilateral triangle of area 1 p 3 (Due to J. Pal in 1921). 2. Kakeya … WebTHE KAKEYA PROBLEM In this lecture, we will discuss Kakeya Conjecture and some known results about it. Definition Suppose that Ti ⊂ Rn are tubes of length N and radius 1. {Ti} is a Kakeya set of tubes if {V(Ti)} is 1 N-separated and 2 N-dense in Sn−1, where V(T i) is
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 length can be turned through 360°. This question was first posed, for convex regions, by Sōichi Kakeya (1917). The minimum area for convex sets is achieved by an … See more 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 … See more 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 … See more Sets containing circles and spheres Analogues of the Kakeya problem include considering sets containing more general shapes than lines, such as circles. • In … See more • Nikodym set See more Statement The same question of how small these Besicovitch sets could be was then posed in higher dimensions, giving rise to a number of … See more 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, Charles Fefferman was able to use the Besicovitch set construction to show that in dimensions … See more 1. ^ Pal, Julius (1920). "Ueber ein elementares variationsproblem". Kongelige Danske Videnskabernes Selskab Math.-Fys. Medd. 2: 1–35. 2. ^ Besicovitch, Abram (1919). "Sur deux questions d'integrabilite des fonctions". J. Soc. Phys. Math. 2: … See more WebSep 24, 2008 · The Kakeya Problem for Simply Connected and for Star-shaped Sets. by Frederick Cunningham, Jr. Year of Award: 1972. Publication Information: The American Mathematical Monthly, vol. 78, 1971, pp. 114-129. Summary: No summary is currently available. Read the Article:
WebOct 15, 2015 · The famed Kakeya Needle Problem, discussed by Charles Fefferman from Princeton University.More links & stuff in full description below ↓↓↓Edit and animation ...
WebMar 15, 2024 · Kakeya needle problem. The Kakeya needle problem asks whether there is a minimum area of a region in the plane, in which a needle of unit length can be turned through 360°. This question was first posed, for convex regions, by Sōichi Kakeya ().The minimum area for convex sets is achieved by an equilateral triangle of height 1 and area 1/ √ 3, as … nsw and wa time differenceWebRecent progress on the Kakeya problem June 11, 2009 1 The flnite fleld Kakeya problem Let Fq denote the flnite fleld of cardinality q.A set K µ Fn q is said to be a Kakeya set if it \contains a line in every direction". In other words, for every \direction" b 2 Fn q there should exist an \ofiset" a 2 Fn q such that the \line" through a in direction b, i.e., the set fa + tbjt 2 … nsw animal registryWebFeb 13, 2013 · The Kakeya problem was proposed in 1917, by the Japanese mathematician Soichi Kakeya. The problem states, In the class of figures in which a segment of length 1 … nike af1 athletic clubWebThe classical Kakeya problem asks how small a set (called a Kakeya set) can be in n-dimensional Euclidean space if it contains a unit line segment in every direction. It is … nsw angler accessWebFeb 16, 2001 · New bounds on Kakeya problems. Nets Katz, Terence Tao. We establish new estimates on the Minkowski and Hausdorff dimensions of Besicovitch sets and obtain new bounds on the Kakeya maximal operator. Comments: 24 pages, 5 figures, submitted, Journal d'Analyse de Jerusalem. Subjects: nike af1 backpack whiteWebThe Kakeya problem is a representative mem-ber of a much larger family of problems of a similar flavour (but with more technical formula-tions). For instance, one can define a fl … nike af1 corduroyWebSōichi Kakeya (掛谷 宗一, Kakeya Sōichi, January 18, 1886 – January 9, 1947) was a Japanese mathematician who worked mainly in mathematical analysis and who posed the Kakeya problem and solved a version of the transportation problem. He received the Imperial Prize of the Japan Academy in 1928, and was elected to the Japan Academy in … nsw and queensland border map