Kakeya set (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Kakeya set" in English language version.

refsWebsite

Global rank English rank

19doi.org

2^nd place

8semanticscholar.org

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8^th place

5arxiv.org

69^th place

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4jstor.org

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4harvard.edu

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2archive.today

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2nih.gov

4^th place

1worldcat.org

5^th place

1uni-muenchen.de

3,337^th place

3,444^th place

1web.archive.org

1^st place

1maa.org

3,479^th place

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1scmp.com

362^nd place

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1jagran.com

1,051^st place

948^th place

1quantamagazine.org

6,413^th place

4,268^th place

1ams.org

451^st place

277^th place

1caltech.edu

887^th place

714^th place

1terrytao.wordpress.com

low place

1weizmann.ac.il

4,983^rd place

8,002^nd place

ams.org

Tao, Terence (March 2001). "From Rotating Needles to Stability of Waves: Emerging Connections between Combinatorics, Analysis and PDE" (PDF). Notices of the AMS. 48 (3): 297–303.

archive.today

"Chinese maths star Wang Hong solves 'infamous' geometry problem". South China Morning Post. 4 March 2025. Archived from the original on 4 March 2025.
"Century-Old Math Enigma Finally Solved: How Chinese Student Cracked An 'Impossible' Geometry Mystery". Dainik Jagran. 4 March 2025. Archived from the original on 4 March 2025.

arxiv.org

Hong Wang; Joshua Zahl (2025-02-24). "Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions". arXiv:2502.17655 [math.CA].
Katz, Nets Hawk; Tao, Terence (2002). "New bounds for Kakeya problems". Journal d'Analyse Mathématique. 87: 231–263. arXiv:math/0102135. doi:10.1007/BF02868476. S2CID 119644987.
Katz, Nets Hawk; Łaba, Izabella; Tao, Terence (September 2000). "An Improved Bound on the Minkowski Dimension of Besicovitch Sets in $\mathbb {R} ^{3}$ ". The Annals of Mathematics. 152 (2): 383–446. arXiv:math/0004015. doi:10.2307/2661389. JSTOR 2661389. S2CID 17007027.
Katz, Nets Hawk; Zahl, Joshua (2019). "An improved bound on the Hausdorff dimension of Besicovitch sets in $\mathbb {R} ^{3}$ ". Journal of the American Mathematical Society. 32 (1): 195–259. arXiv:1704.07210. doi:10.1090/jams/907. S2CID 119322412.
Dvir, Z. (2009). "On the size of Kakeya sets in finite fields". Journal of the American Mathematical Society. 22 (4): 1093–1097. arXiv:0803.2336. Bibcode:2009JAMS...22.1093D. doi:10.1090/S0894-0347-08-00607-3. S2CID 3358826.

caltech.edu

authors.library.caltech.edu

Wolff, Thomas; Wolff, Thomas (1999). "On some variants of the Kakeya problem" (PDF). Pacific Journal of Mathematics. 190: 111–154. doi:10.2140/pjm.1999.190.111.

doi.org

Besicovitch, A. S. (August 1963). "The Kakeya Problem". The American Mathematical Monthly. 70 (7): 697–706. doi:10.2307/2312249. ISSN 0002-9890. JSTOR 2312249.
Besicovitch, Abram (1919). "Sur deux questions d'integrabilite des fonctions". J. Soc. Phys. Math. 2: 105–123.
Besicovitch, Abram (1928). "On Kakeya's problem and a similar one". Mathematische Zeitschrift. 27: 312–320. doi:10.1007/BF01171101. S2CID 121781065.
Perron, O. (1928). "Über einen Satz von Besicovitch". Mathematische Zeitschrift. 28: 383–386. doi:10.1007/BF01181172. S2CID 120768630.
Falconer, K. J. (1985). The Geometry of Fractal Sets. Cambridge University Press. pp. 96–99.
Cunningham, F. (1971). "The Kakeya problem for simply connected and for star-shaped sets" (PDF). American Mathematical Monthly. 78 (2). The American Mathematical Monthly, Vol. 78, No. 2: 114–129. doi:10.2307/2317619. JSTOR 2317619.
Davies, Roy (1971). "Some remarks on the Kakeya problem". Mathematical Proceedings of the Cambridge Philosophical Society. 69 (3): 417–421. Bibcode:1971PCPS...69..417D. doi:10.1017/S0305004100046867.
Wolff, Thomas (1995). "An improved bound for Kakeya type maximal functions". Rev. Mat. Iberoamericana. 11 (3): 651–674. doi:10.4171/rmi/188.
Katz, Nets Hawk; Tao, Terence (2002). "New bounds for Kakeya problems". Journal d'Analyse Mathématique. 87: 231–263. arXiv:math/0102135. doi:10.1007/BF02868476. S2CID 119644987.
Katz, Nets Hawk; Łaba, Izabella; Tao, Terence (September 2000). "An Improved Bound on the Minkowski Dimension of Besicovitch Sets in $\mathbb {R} ^{3}$ ". The Annals of Mathematics. 152 (2): 383–446. arXiv:math/0004015. doi:10.2307/2661389. JSTOR 2661389. S2CID 17007027.
Katz, Nets Hawk; Zahl, Joshua (2019). "An improved bound on the Hausdorff dimension of Besicovitch sets in $\mathbb {R} ^{3}$ ". Journal of the American Mathematical Society. 32 (1): 195–259. arXiv:1704.07210. doi:10.1090/jams/907. S2CID 119322412.
Fefferman, Charles (1971). "The multiplier problem for the ball". Annals of Mathematics. 94 (2): 330–336. doi:10.2307/1970864. JSTOR 1970864.
Wolff, Thomas (1997). "A Kakeya problem for circles". American Journal of Mathematics. 119 (5): 985–1026. doi:10.1353/ajm.1997.0034. S2CID 120122372.
Wolff, Thomas; Wolff, Thomas (1999). "On some variants of the Kakeya problem" (PDF). Pacific Journal of Mathematics. 190: 111–154. doi:10.2140/pjm.1999.190.111.
Stein, Elias (1976). "Maximal functions: Spherical means". Proc. Natl. Acad. Sci. U.S.A. 73 (7): 2174–2175. Bibcode:1976PNAS...73.2174S. doi:10.1073/pnas.73.7.2174. PMC 430482. PMID 16592329.
Marstrand, J. M. (1987). "Packing circles in the plane". Proceedings of the London Mathematical Society. 55: 37–58. doi:10.1112/plms/s3-55.1.37.
Marstrand, J. M. (1979). "Packing Planes in $\mathbb {R} ^{3}$ ". Mathematika. 26 (2): 180–183. doi:10.1112/S0025579300009748.
Falconer, K. J. (1980). "Continuity properties of k-plane integrals and Besicovitch sets". Mathematical Proceedings of the Cambridge Philosophical Society. 87 (2): 221–226. Bibcode:1980MPCPS..87..221F. doi:10.1017/S0305004100056681.
Bourgain, Jean (1997). "Besicovitch type maximal operators and applications to Fourier analysis". Geometric and Functional Analysis. 1 (2): 147–187. doi:10.1007/BF01896376. S2CID 122038469.
Dvir, Z. (2009). "On the size of Kakeya sets in finite fields". Journal of the American Mathematical Society. 22 (4): 1093–1097. arXiv:0803.2336. Bibcode:2009JAMS...22.1093D. doi:10.1090/S0894-0347-08-00607-3. S2CID 3358826.

dx.doi.org

Besicovitch, A. S. (August 1963). "The Kakeya Problem". The American Mathematical Monthly. 70 (7): 697–706. doi:10.2307/2312249. ISSN 0002-9890. JSTOR 2312249.

harvard.edu

ui.adsabs.harvard.edu

Davies, Roy (1971). "Some remarks on the Kakeya problem". Mathematical Proceedings of the Cambridge Philosophical Society. 69 (3): 417–421. Bibcode:1971PCPS...69..417D. doi:10.1017/S0305004100046867.
Stein, Elias (1976). "Maximal functions: Spherical means". Proc. Natl. Acad. Sci. U.S.A. 73 (7): 2174–2175. Bibcode:1976PNAS...73.2174S. doi:10.1073/pnas.73.7.2174. PMC 430482. PMID 16592329.
Falconer, K. J. (1980). "Continuity properties of k-plane integrals and Besicovitch sets". Mathematical Proceedings of the Cambridge Philosophical Society. 87 (2): 221–226. Bibcode:1980MPCPS..87..221F. doi:10.1017/S0305004100056681.
Dvir, Z. (2009). "On the size of Kakeya sets in finite fields". Journal of the American Mathematical Society. 22 (4): 1093–1097. arXiv:0803.2336. Bibcode:2009JAMS...22.1093D. doi:10.1090/S0894-0347-08-00607-3. S2CID 3358826.

jagran.com

english.jagran.com

"Century-Old Math Enigma Finally Solved: How Chinese Student Cracked An 'Impossible' Geometry Mystery". Dainik Jagran. 4 March 2025. Archived from the original on 4 March 2025.

jstor.org

Besicovitch, A. S. (August 1963). "The Kakeya Problem". The American Mathematical Monthly. 70 (7): 697–706. doi:10.2307/2312249. ISSN 0002-9890. JSTOR 2312249.
Cunningham, F. (1971). "The Kakeya problem for simply connected and for star-shaped sets" (PDF). American Mathematical Monthly. 78 (2). The American Mathematical Monthly, Vol. 78, No. 2: 114–129. doi:10.2307/2317619. JSTOR 2317619.
Katz, Nets Hawk; Łaba, Izabella; Tao, Terence (September 2000). "An Improved Bound on the Minkowski Dimension of Besicovitch Sets in $\mathbb {R} ^{3}$ ". The Annals of Mathematics. 152 (2): 383–446. arXiv:math/0004015. doi:10.2307/2661389. JSTOR 2661389. S2CID 17007027.
Fefferman, Charles (1971). "The multiplier problem for the ball". Annals of Mathematics. 94 (2): 330–336. doi:10.2307/1970864. JSTOR 1970864.

maa.org

Cunningham, F. (1971). "The Kakeya problem for simply connected and for star-shaped sets" (PDF). American Mathematical Monthly. 78 (2). The American Mathematical Monthly, Vol. 78, No. 2: 114–129. doi:10.2307/2317619. JSTOR 2317619.

nih.gov

ncbi.nlm.nih.gov

Stein, Elias (1976). "Maximal functions: Spherical means". Proc. Natl. Acad. Sci. U.S.A. 73 (7): 2174–2175. Bibcode:1976PNAS...73.2174S. doi:10.1073/pnas.73.7.2174. PMC 430482. PMID 16592329.

pubmed.ncbi.nlm.nih.gov

Stein, Elias (1976). "Maximal functions: Spherical means". Proc. Natl. Acad. Sci. U.S.A. 73 (7): 2174–2175. Bibcode:1976PNAS...73.2174S. doi:10.1073/pnas.73.7.2174. PMC 430482. PMID 16592329.

quantamagazine.org

Howlett, Joseph (2025-03-14). "'Once in a Century' Proof Settles Math's Kakeya Conjecture". Quanta Magazine. Retrieved 2025-03-21.

scmp.com

"Chinese maths star Wang Hong solves 'infamous' geometry problem". South China Morning Post. 4 March 2025. Archived from the original on 4 March 2025.

semanticscholar.org

api.semanticscholar.org

Besicovitch, Abram (1919). "Sur deux questions d'integrabilite des fonctions". J. Soc. Phys. Math. 2: 105–123.
Besicovitch, Abram (1928). "On Kakeya's problem and a similar one". Mathematische Zeitschrift. 27: 312–320. doi:10.1007/BF01171101. S2CID 121781065.
Perron, O. (1928). "Über einen Satz von Besicovitch". Mathematische Zeitschrift. 28: 383–386. doi:10.1007/BF01181172. S2CID 120768630.
Falconer, K. J. (1985). The Geometry of Fractal Sets. Cambridge University Press. pp. 96–99.
Katz, Nets Hawk; Tao, Terence (2002). "New bounds for Kakeya problems". Journal d'Analyse Mathématique. 87: 231–263. arXiv:math/0102135. doi:10.1007/BF02868476. S2CID 119644987.
Katz, Nets Hawk; Łaba, Izabella; Tao, Terence (September 2000). "An Improved Bound on the Minkowski Dimension of Besicovitch Sets in $\mathbb {R} ^{3}$ ". The Annals of Mathematics. 152 (2): 383–446. arXiv:math/0004015. doi:10.2307/2661389. JSTOR 2661389. S2CID 17007027.
Katz, Nets Hawk; Zahl, Joshua (2019). "An improved bound on the Hausdorff dimension of Besicovitch sets in $\mathbb {R} ^{3}$ ". Journal of the American Mathematical Society. 32 (1): 195–259. arXiv:1704.07210. doi:10.1090/jams/907. S2CID 119322412.
Wolff, Thomas (1997). "A Kakeya problem for circles". American Journal of Mathematics. 119 (5): 985–1026. doi:10.1353/ajm.1997.0034. S2CID 120122372.
Bourgain, Jean (1997). "Besicovitch type maximal operators and applications to Fourier analysis". Geometric and Functional Analysis. 1 (2): 147–187. doi:10.1007/BF01896376. S2CID 122038469.
Dvir, Z. (2009). "On the size of Kakeya sets in finite fields". Journal of the American Mathematical Society. 22 (4): 1093–1097. arXiv:0803.2336. Bibcode:2009JAMS...22.1093D. doi:10.1090/S0894-0347-08-00607-3. S2CID 3358826.

terrytao.wordpress.com

Terence Tao (2008-03-24). "Dvir's proof of the finite field Kakeya conjecture". What's New. Retrieved 2008-04-08.

uni-muenchen.de

mathematik.uni-muenchen.de

The Kakeya Problem Archived 2015-07-15 at the Wayback Machine by Markus Furtner

web.archive.org

The Kakeya Problem Archived 2015-07-15 at the Wayback Machine by Markus Furtner

weizmann.ac.il

eccc.weizmann.ac.il

Dvir, Zeev (2009). "From Randomness Extraction to Rotating Needles". ACM SIGACT News. ECCC TR09-077..

worldcat.org

search.worldcat.org

Besicovitch, A. S. (August 1963). "The Kakeya Problem". The American Mathematical Monthly. 70 (7): 697–706. doi:10.2307/2312249. ISSN 0002-9890. JSTOR 2312249.