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math.MG2022★ 3 cited
Equivalences between different forms of the Kakeya conjecture and duality of Hausdorff and packing dimensions for additive complements
Tamás Keleti, András Máthé
The Kakeya conjecture is generally formulated as one the following statements: every compact/Borel/arbitrary subset of that contains a (unit) line segment in every…
math.MG2022★ 4 cited
Circle Squaring with Pieces of Small Boundary and Low Borel Complexity
András Máthé, Jonathan A. Noel, Oleg Pikhurko
Tarski's Circle Squaring Problem from 1925 asks whether it is possible to partition a disk in the plane into finitely many pieces and reassemble them via isometries to yield a part…