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The Kakeya Problem for Circular Arcs

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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.

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References

  1. Besicovitch A.S.: On Kakeya’s problem and a similar one. Math. Z. 27, 312–320 (1928)

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  4. M. Csörnyei, K. Héra and M. Laczkovich, Closed sets with the Kakeya property, to appear in Mathematika.

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Authors and Affiliations

  1. Department of Analysis, Institute of Mathematics, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/C, 1117, Hungary

    K. Héra & M. Laczkovich

Authors
  1. K. Héra
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  2. M. Laczkovich
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Corresponding author

Correspondence to K. Héra.

Additional information

The research of the second author was partially supported by the Hungarian National Research, Development and Innovation Office, Grant No. NKFIH 104178.

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Héra, K., Laczkovich, M. The Kakeya Problem for Circular Arcs. Acta Math. Hungar. 150, 479–511 (2016). https://doi.org/10.1007/s10474-016-0663-5

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  • DOI: https://doi.org/10.1007/s10474-016-0663-5

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