Recent progress on the Kakeya conjecture

N. Katz, Terence Tao

Type: Article

Publication Date: 2002-06-01

Citations: 52

DOI: https://doi.org/10.5565/publmat_esco02_07

Abstract

We survey recent developments on the Kakeya problem. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

Locations

Publicacions Matemàtiques - View
LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) - View - PDF
arXiv (Cornell University) - PDF
arXiv (Cornell University) - View
Publicacions Matemàtiques - View
LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) - View - PDF
arXiv (Cornell University) - PDF
arXiv (Cornell University) - View
Publicacions Matemàtiques - View
LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) - View - PDF
arXiv (Cornell University) - PDF
arXiv (Cornell University) - View

Similar Works

Action	Title	Year	Authors
+	A Remark on the Kakeya Problem	1963	A. A. Blank
+	A Remark on the Kakeya Problem	1963	Albert A. Blank
+	A Note on Kakeya's Theorem on Algebraic Equations	1931	Shin-ichi Takaiiashi
+	Recent progress on the Kakeya conjecture	2000	Nets Hawk Katz Terence Tao
+	The inverse Kakeya problem	2021	Sergio Cabello Otfried Cheong Michael Gene Dobbins
+	On some aspects of the Kegel–Wielandt $$\sigma $$-problem	2023	Zh. Xu X. Yi С. Ф. Каморников
+	Notes on computation of Kakutani fixed points	1996	Zeke Wang
+	Notes on Computation of Kakutani Fixed Points	1996	W ZEKE
+	On a variant of the Kakeya problem in $${\mathbb{R}}$$ R	2013	Yu Deng HU Cai-hong Shunchao Long Tai‐Man Tang Jörg Μ. Thuswaldner Lifeng Xi
+	Recent Advances in Harmonic Analysis and Partial Differential Equations in Contemporary Mathematics	2012	Andrea R. Nahmod Christopher D. Sogge Xiaoyi Zhang Shijun Zheng
+	On a generalization of the EnestrÃ¶m-Kakeya theorem	1992	KovaÄ eviÄ‡ MilovanoviÄ‡ I.å ⁄ .
+ PDF	About an old problem of Karamata	2002	Slavko Simić
+	Fixed Point Results Based on the Ważewski Method	2005	Roman Srzednicki Klaudiusz Wójcik Piotr Zgliczyśki
+	Function spaces, harmonic analysis, and differential equations : collected papers dedicated to the 95th birthday of Academician Sergei Mikhailovich Nikol'skii	2001	Sergei M Nikol'skii Маик Наука
+	An Application of the Kakeya-Enestrom Theorem.	2004	Jalal Karam
+	KC Sinha Maths Solutions Class 10 Chapter 2 Polynomials Ex 2.1	2019	Ram Ram
+ PDF	About the regularizing properties of the non-cut-off Kac equation	1995	Laurent Desvillettes
+	SOME GENERALIZATIONS OF THE ENESTR()M-KAKEYA THEOREM	1997	Robert B. Gardner N. K. Govil
+	A Family of Fractal Fourier Restriction Estimates with Implications on the Kakeya Problem	2024	Bassam Shayya
+	The Finite Field Kakeya Problem	2001	Keith M. Rogers

Works That Cite This (51)

Action	Title	Year	Authors
+	Some results in support of the Kakeya Conjecture	2014	Jonathan M. Fraser Eric J. Olson James C. Robinson
+	An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³	2018	Nets Hawk Katz Joshua Zahl
+	Pointwise convergence of noncommutative Fourier series	2019	Guixiang Hong Simeng Wang Xumin Wang
+	An improved bound on the Hausdorff dimension of Besicovitch sets in $\mathbb{R}^3$	2017	Nets Hawk Katz Joshua Zahl
+	A Kakeya maximal function estimate in four dimensions using planebrushes	2019	Nets Hawk Katz Joshua Zahl
+ PDF	Some Results in Support of the Kakeya Conjecture	2017	Jonathan M. Fraser Olson Robinson
+	Finite field models in additive combinatorics	2005	Ben Green
+	Improved variable coefficient square functions and local smoothing of Fourier integral operators	2019	Chuanwei Gao Changxing Miao Jianwei-Urbain Yang
+ PDF	Анализ Фурье в комбинаторной теории чисел	2010	Илья Дмитриевич Шкредов Ilya D. Shkredov
+	Estimaciones de dimensión para conjuntos de tipo Furstenberg y teoremas de restricción para medidas de Hausdorff	2010	Ezequiel Rela

Works Cited by This (26)

Action	Title	Year	Authors
+ PDF	Recent work connected with the Kakeya problem	2003	Thomas Wolff
+	Sums of Finite Sets	1996	Imre Z. Ruzsa
+	None	1999	Thomas Wolff
+	Maximal operators related to the Radon transform and the Calderon-Zygmund method of rotations	1986	Michael Christ Javier Duoandikoetxea José L. Rubio de Francia
+ PDF	$L^{p}$ estimates for the $X$-ray transform	1983	S.W. Drury
+	An x-ray estimate in $R^n$	1999	Izabella Łaba Terence Tao
+	From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE	2000	Terence Tao
+ PDF	An improved bound for Kakeya type maximal functions	1995	Thomas Wolff
+ PDF Chat	New bounds for Kakeya problems	2002	N. Katz Terence Tao
+	Besicovitch type maximal operators and applications to fourier analysis	1991	Jean Bourgain