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Acta Mathematica Hungarica

, Volume 150, Issue 2, pp 479–511 | Cite as

The Kakeya Problem for Circular Arcs

  • K. Héra
  • M. Laczkovich
Article

Abstract

We prove that if a circular arc has angle short enough, then it can be continuously moved to any prescribed position within a set of arbitrarily small area.

Key words and phrases

Kakeya problem for circular arcs 

Mathematics Subject Classification

28A75 

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References

  1. 1.
    Besicovitch A.S.: On Kakeya’s problem and a similar one. Math. Z. 27, 312–320 (1928)MathSciNetCrossRefzbMATHGoogle Scholar
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    Cunningham F. Jr.: The Kakeya problem for simply connected and for star-shaped sets. Amer. Math. Monthly 78, 114–129 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
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    Cunningham F. Jr.: Three Kakeya problems. Amer. Math. Monthly 81, 582–592 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    M. Csörnyei, K. Héra and M. Laczkovich, Closed sets with the Kakeya property, to appear in Mathematika.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Department of Analysis, Institute of MathematicsEötvös Loránd UniversityBudapestHungary

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