Ruixiang Zhang

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math.CA2025

Power loss for the Mizohata-Takeuchi conjecture on $C^{k}$ convex hypersurfaces

Hannah Cairo, Ruixiang Zhang

We find a family of compact $C^{k}$ hypersurfaces where the local Mizohata-Takeuchi Conjecture fails with a power loss of $R^{α}$ for any $α < \frac{n - 1}{n - 1 + k}$ . Moreover, this family i…

math.CA2019

Improved bounds for the Kakeya maximal conjecture in higher dimensions

Jonathan Hickman, Keith M. Rogers, Ruixiang Zhang

We adapt Guth's polynomial partitioning argument for the Fourier restriction problem to the context of the Kakeya problem. By writing out the induction argument as a recursive algo…

Power loss for the Mizohata-Takeuchi conjecture on Ck convex hypersurfaces

Improved bounds for the Kakeya maximal conjecture in higher dimensions

Power loss for the Mizohata-Takeuchi conjecture on $C^{k}$ convex hypersurfaces