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math.CA2026
On planar Nikodym-type sets
Alan Chang, Mingfeng Chen, Shaoming Guo +3
Nikodym constructed a measure-zero Borel set in the plane that contains a punctured line segment passing through each point in the unit square. Fenton and Falconer asked whether a…
math.CA2026
Curved Kakeya problems and the projective geometry of paths
Shaoming Guo, Larry Guth, Arian Nadjimzadah +2
We introduce a general framework for curved Kakeya problems in , encompassing those arising from Hörmander-type oscillatory integrals. Every family of curves determin…