Develops a quantitative flatness framework to obstruct Fourier restriction, L^p-improving, and Fourier decay estimates for measures, applied to bound Fourier dimensions of surfaces, curves, Patterson-Sullivan measures, and self-affine sets.
Uniformly perfect measures on strictly convex planar graphs arel 2-flattening.https://arxiv.org/pdf/2509.09354,
2 Pith papers cite this work. Polarity classification is still indexing.
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2026 2verdicts
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Improves the decoupling exponent for AD-regular arc collections on the parabola via Szemerédi-Trotter estimates inside a bootstrapping argument from prior work, with applications to arithmetic Cantor sets.
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Quantitative flatness and obstructions in Fourier analysis
Develops a quantitative flatness framework to obstruct Fourier restriction, L^p-improving, and Fourier decay estimates for measures, applied to bound Fourier dimensions of surfaces, curves, Patterson-Sullivan measures, and self-affine sets.
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Decoupling for AD-regular sets on the parabola
Improves the decoupling exponent for AD-regular arc collections on the parabola via Szemerédi-Trotter estimates inside a bootstrapping argument from prior work, with applications to arithmetic Cantor sets.