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arXiv · 2502.06137

A Counterexample to the Mizohata-Takeuchi Conjecture

Hannah Cairo
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Abstract

We derive a family of $L^p$ estimates of the X-Ray transform of positive measures in $\mathbb R^d$, which we use to construct a $\log R$-loss counterexample to the Mizohata-Takeuchi conjecture for every $C^2$ hypersurface in $\mathbb R^d$ that does not lie in a hyperplane. In particular, multilinear restriction estimates at the endpoint cannot be sharpened directly by the Mizohata-Takeuchi conjecture.

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Hannah Cairo. 2025-02-10. A Counterexample to the Mizohata-Takeuchi Conjecture. https://arxiv.org/abs/2502.06137

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