A counterexample to the Mizohata-Takeuchi Conjecture

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

Comments: 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.

OARS Online Analysis Research Seminar

Series comments: Visit our homepage for further information. Some recordings available on YouTube