The Kakeya Problem for Circular Arcs

@article{Hra2016TheKP,
  title={The Kakeya Problem for Circular Arcs},
  author={K. H{\'e}ra and Mikl{\'o}s Laczkovich},
  journal={Acta Mathematica Hungarica},
  year={2016},
  volume={150},
  pages={479-511}
}
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

SHOWING 1-5 OF 5 REFERENCES
Closed sets with the Kakeya property
We say that a planar set $A$ has the Kakeya property if there exist two different positions of $A$ such that $A$ can be continuously moved from the first position to the second within a set of
On Kakeya's problem and a similar one
Besicovitch, On Kakeya’s problem and a similar
  • one, Math. Z
  • 1928
Three Kakeya Problems