H. Cairo

collaborators

2 papers

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 $R^{I^} \pm$ for any $I^\pm < \frac{n - 1}{n - 1 + k}$ . Moreover, this family…

math.CA2025

A Counterexample to the Mizohata-Takeuchi Conjecture

Hannah Cairo

We derive a family of $L^{p}$ estimates of the X-Ray transform of positive measures in $R^{d}$ , which we use to construct a $lo g R$ -loss counterexample to the Mizohata-Takeuch…

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

A Counterexample to the Mizohata-Takeuchi Conjecture

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