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A Kakeya-type problem for circles

From: American Journal of Mathematics
Volume 119, Number 5, October 1997
pp. 985-1026 | 10.1353/ajm.1997.0034



We prove full Hausdorff dimension in a variant of the Kakeya problem involving circles in the plane, and also sharp estimates for the relevant maximal function. These results can also be formulated in terms of the wave equation in two space variables. A novelty in our approach is the use of ideas from computational geometry.